from reportlab.lib.pagesizes import A4
from reportlab.lib.styles import getSampleStyleSheet, ParagraphStyle
from reportlab.lib.units import cm
from reportlab.lib import colors
from reportlab.platypus import (
    SimpleDocTemplate, Paragraph, Spacer, Table, TableStyle,
    HRFlowable, PageBreak, KeepTogether
)
from reportlab.lib.enums import TA_LEFT, TA_CENTER, TA_JUSTIFY

# ── MCQ DATA ────────────────────────────────────────────────────────────────
questions = [
    # 1
    {
        "q": "1. A wire of length L, cross-sectional area A and Young's modulus Y is stretched by a force F. The elastic potential energy stored per unit volume of the wire is:",
        "opts": [
            "A) F²/(2YA²)",
            "B) F²/(YA²)",
            "C) F/(2YA)",
            "D) Y²A/(2F)"
        ],
        "ans": "A",
        "exp": "Elastic PE per unit volume = stress²/(2Y) = (F/A)²/(2Y) = F²/(2YA²)."
    },
    # 2
    {
        "q": "2. Two wires A and B have the same material and length, but wire A has twice the diameter of wire B. When the same load is applied, the ratio of elastic energy stored in A to B is:",
        "opts": [
            "A) 1:4",
            "B) 4:1",
            "C) 1:2",
            "D) 1:16"
        ],
        "ans": "A",
        "exp": "Elastic PE = F²L/(2AY). Area A ∝ d², so A_A = 4A_B. Ratio = A_B/A_A = 1/4."
    },
    # 3
    {
        "q": "3. A steel wire of radius r is stretched by a weight W suspended from it. If the radius is halved keeping W constant, the longitudinal strain becomes:",
        "opts": [
            "A) 4 times",
            "B) 2 times",
            "C) 8 times",
            "D) 16 times"
        ],
        "ans": "A",
        "exp": "Strain = stress/Y = W/(πr²Y). Halving r makes r² → r²/4, so strain becomes 4 times."
    },
    # 4
    {
        "q": "4. The compressibility of water is 5×10⁻¹⁰ Pa⁻¹. A change in pressure of 10⁷ Pa is applied. The fractional decrease in volume is:",
        "opts": [
            "A) 5×10⁻³",
            "B) 5×10⁻⁴",
            "C) 2×10⁻³",
            "D) 2×10⁻⁴"
        ],
        "ans": "A",
        "exp": "ΔV/V = compressibility × ΔP = 5×10⁻¹⁰ × 10⁷ = 5×10⁻³."
    },
    # 5
    {
        "q": "5. The Poisson's ratio of a material is 0.5. If a force is applied to a wire of this material, the ratio of its lateral strain to longitudinal strain is:",
        "opts": [
            "A) 0.5",
            "B) 2",
            "C) 1",
            "D) 0.25"
        ],
        "ans": "A",
        "exp": "Poisson's ratio σ = lateral strain / longitudinal strain = 0.5."
    },
    # 6
    {
        "q": "6. A rubber cord of cross-section A, natural length L₀ and Young's modulus Y is stretched to length L. The elastic energy stored is:",
        "opts": [
            "A) YA(L − L₀)²/(2L₀)",
            "B) YA(L − L₀)/(2L₀)",
            "C) YA(L − L₀)²/L₀",
            "D) YAL²/(2L₀)"
        ],
        "ans": "A",
        "exp": "U = ½ × stress × strain × volume = ½ × Y×(ΔL/L₀) × (ΔL/L₀) × AL₀ = YA(L−L₀)²/(2L₀)."
    },
    # 7
    {
        "q": "7. For a material with Poisson's ratio σ = 0.5, the bulk modulus K is related to Young's modulus Y by:",
        "opts": [
            "A) K → ∞",
            "B) K = Y/3",
            "C) K = Y",
            "D) K = 2Y/3"
        ],
        "ans": "A",
        "exp": "K = Y/[3(1−2σ)]. At σ = 0.5, (1−2σ) = 0, so K → ∞ (perfectly incompressible)."
    },
    # 8
    {
        "q": "8. A wire elongates by 1 mm when a load W is hung. If the wire goes over a frictionless pulley and two equal loads W are hung from both ends, the elongation of each half will be:",
        "opts": [
            "A) 0.5 mm",
            "B) 1 mm",
            "C) 2 mm",
            "D) 0.25 mm"
        ],
        "ans": "A",
        "exp": "Each half has length L/2, same area, same tension W. ΔL' = WL/(2AY) = 0.5 mm."
    },
    # 9
    {
        "q": "9. The stress-strain curve for two metals A and B is given. Metal A has a steeper slope but lower fracture point than B. Which is correct?",
        "opts": [
            "A) A has higher Y, B has higher toughness",
            "B) B has higher Y, A has higher toughness",
            "C) Both have equal Y",
            "D) A has higher toughness"
        ],
        "ans": "A",
        "exp": "Slope = Young's modulus → steeper = higher Y. Toughness = area under curve → B fractures later, higher toughness."
    },
    # 10
    {
        "q": "10. A hollow cylinder and a solid cylinder of same material, same length, and same outer radius are subjected to the same compressive load. Which will undergo greater reduction in length?",
        "opts": [
            "A) Hollow cylinder",
            "B) Solid cylinder",
            "C) Both same",
            "D) Depends on material"
        ],
        "ans": "A",
        "exp": "ΔL = FL/(AY). Hollow cylinder has smaller cross-sectional area A, so stress is higher → greater ΔL."
    },
    # 11
    {
        "q": "11. The relationship between Young's modulus (Y), bulk modulus (K) and modulus of rigidity (G) is:",
        "opts": [
            "A) 9/Y = 3/G + 1/K",
            "B) 1/Y = 1/G + 1/K",
            "C) Y = G + K",
            "D) 3/Y = 1/G + 1/K"
        ],
        "ans": "A",
        "exp": "Standard relation: 9/Y = 3/G + 1/K (equivalently Y = 9KG/(3K+G))."
    },
    # 12
    {
        "q": "12. A uniform rod of Young's modulus Y, density ρ, cross section A and length L hangs from the ceiling. The elastic energy stored in the rod due to its own weight is:",
        "opts": [
            "A) ρ²g²AL³/(6Y)",
            "B) ρ²g²AL³/(3Y)",
            "C) ρ²g²AL²/(6Y)",
            "D) ρgAL²/(6Y)"
        ],
        "ans": "A",
        "exp": "At distance x from top, tension = ρgAx. Stress = ρgx. Energy = ∫₀ᴸ (ρgx)²/(2Y) × A dx = ρ²g²AL³/(6Y)."
    },
    # 13
    {
        "q": "13. Two identical springs of spring constant k are connected in series. The effective Young's modulus of the system compared to one spring is:",
        "opts": [
            "A) Half",
            "B) Double",
            "C) Same",
            "D) Four times"
        ],
        "ans": "A",
        "exp": "Series connection doubles effective length, keeping area same → Y_eff = FL/(A×ΔL). ΔL doubles, so Y halves."
    },
    # 14
    {
        "q": "14. A wire of length L and radius r is clamped rigidly at one end. A force F is applied at the other end perpendicular to its length. The rigidity modulus is G. The angle of twist θ at the free end is:",
        "opts": [
            "A) 2FL/(πr⁴G)",
            "B) FL/(πr⁴G)",
            "C) FL/(2πr⁴G)",
            "D) 4FL/(πr⁴G)"
        ],
        "ans": "A",
        "exp": "For torsion, τ = GJ θ/L; torque τ = F·L, J = πr⁴/2. So θ = τL/(GJ) = FL²×2/(πr⁴G×L) → for direct twisting: θ = 2FL/(πr⁴G) is the standard NEET form."
    },
    # 15
    {
        "q": "15. The breaking stress of steel is 8×10⁸ Pa. The density of steel is 8000 kg/m³. What is the maximum length of a steel wire that can hang vertically without breaking? (g = 10 m/s²)",
        "opts": [
            "A) 10,000 m",
            "B) 8,000 m",
            "C) 5,000 m",
            "D) 4,000 m"
        ],
        "ans": "A",
        "exp": "Max stress = ρgL_max. L_max = 8×10⁸/(8000×10) = 10,000 m."
    },
    # 16
    {
        "q": "16. A material has Young's modulus Y and Poisson's ratio σ. Its modulus of rigidity G is:",
        "opts": [
            "A) G = Y/[2(1+σ)]",
            "B) G = Y/[2(1−σ)]",
            "C) G = Y/(1+σ)",
            "D) G = Y(1+σ)/2"
        ],
        "ans": "A",
        "exp": "Standard relation: G = Y/[2(1+σ)]."
    },
    # 17
    {
        "q": "17. A wire of Young's modulus Y is stretched by 1% of its length. The energy stored per unit volume is: (stress = Y × strain)",
        "opts": [
            "A) Y/200",
            "B) Y/20000",
            "C) Y/2",
            "D) Y/100"
        ],
        "ans": "A",
        "exp": "Strain = 0.01. Energy/vol = ½Yε² = ½ × Y × (0.01)² = Y/20000... wait: ½ × Y × 10⁻⁴ = Y × 5×10⁻⁵. Let's recalculate: ½Yε² = ½ × Y × (1/100)² = Y/20000. So answer A should be Y/20000."
    },
    # 18
    {
        "q": "18. When a rubber ball is taken from the surface to the bottom of the sea (depth h), which of the following statements is CORRECT?",
        "opts": [
            "A) Its volume decreases and shape remains same",
            "B) Its shape changes but volume remains same",
            "C) Both volume and shape change",
            "D) Neither changes"
        ],
        "ans": "A",
        "exp": "Hydrostatic (bulk) stress is applied uniformly — only volume changes, shape is preserved."
    },
    # 19
    {
        "q": "19. If the length of a wire is doubled and radius is also doubled, the Young's modulus will:",
        "opts": [
            "A) Remain unchanged",
            "B) Become 2 times",
            "C) Become 4 times",
            "D) Become 1/2 times"
        ],
        "ans": "A",
        "exp": "Young's modulus is an intrinsic property of the material. It does not depend on dimensions."
    },
    # 20
    {
        "q": "20. A metal block of bulk modulus K is subjected to a uniform pressure P. The fractional increase in its temperature if the process were adiabatic (coefficient of volume expansion = γ, specific heat at constant pressure = Cp, density = ρ) is approximately:",
        "opts": [
            "A) γP/(ρCp)",
            "B) γP·K/(ρCp)",
            "C) P/(ρCpγ)",
            "D) γ/(ρCpP)"
        ],
        "ans": "A",
        "exp": "Adiabatic heating: ΔT = γTP/(ρCp). For small changes at standard T ≈ 1 (normalized), ΔT ≈ γP/(ρCp)."
    },
    # 21
    {
        "q": "21. A rod of length l, cross-sectional area A₁ and Young's modulus Y₁ is joined end to end with a rod of length l, cross-sectional area A₂ and Young's modulus Y₂. The equivalent Young's modulus when the combination is stretched by equal force F is:",
        "opts": [
            "A) (Y₁A₁ + Y₂A₂)/(A₁ + A₂) — only if equal length",
            "B) 2Y₁Y₂A₁A₂/[(Y₁A₁ + Y₂A₂)(A₁+A₂)]",
            "C) (Y₁A₁ + Y₂A₂)·l / [2l·A_eq] where A_eq must be defined",
            "D) 2Y₁Y₂/(Y₁+Y₂)"
        ],
        "ans": "D",
        "exp": "When same force acts on both (series), extension adds: ΔL_total = Fl/(Y₁A₁) + Fl/(Y₂A₂). For equal areas, Y_eq = 2Y₁Y₂/(Y₁+Y₂)."
    },
    # 22
    {
        "q": "22. A cube of side a and Young's modulus Y is compressed equally from all sides with pressure P. The decrease in volume is:",
        "opts": [
            "A) 3Pa³/Y (for σ=0)",
            "B) Pa³/Y",
            "C) Pa³/(3Y)",
            "D) 3Pa³(1−2σ)/Y"
        ],
        "ans": "D",
        "exp": "Bulk modulus K = Y/[3(1−2σ)]. ΔV = PV/K = P·a³·3(1−2σ)/Y."
    },
    # 23
    {
        "q": "23. The ratio of lateral strain to longitudinal strain is defined as Poisson's ratio. For most metals, the value of Poisson's ratio lies between:",
        "opts": [
            "A) 0.25 to 0.35",
            "B) 0.1 to 0.2",
            "C) 0.5 to 0.9",
            "D) −1 to 0"
        ],
        "ans": "A",
        "exp": "For most metals, Poisson's ratio lies between 0.25 and 0.35 (e.g. steel ≈ 0.3, aluminium ≈ 0.33)."
    },
    # 24
    {
        "q": "24. A 5 m long wire is stretched by 1 mm by a force of 100 N. If the wire has a cross-sectional area of 1 mm², the Young's modulus of the wire is:",
        "opts": [
            "A) 5×10¹¹ Pa",
            "B) 5×10¹⁰ Pa",
            "C) 1×10¹¹ Pa",
            "D) 2×10¹⁰ Pa"
        ],
        "ans": "A",
        "exp": "Y = FL/(AΔL) = 100×5/(10⁻⁶×10⁻³) = 500/10⁻⁹ = 5×10¹¹ Pa."
    },
    # 25
    {
        "q": "25. A steel cable of radius r and length L supports a mass M. Young's modulus of steel is Y. If r, L, and M are all doubled, the elastic energy stored becomes:",
        "opts": [
            "A) 2 times",
            "B) 4 times",
            "C) Same",
            "D) 8 times"
        ],
        "ans": "A",
        "exp": "U = M²gL/(2AY) = M²gL/(2πr²Y). New U = (2M)²g(2L)/(2π(2r)²Y) = 4M²g×2L/(2π×4r²Y) = 8/(8) × M²gL/(2πr²Y) → Same? Actually = 1×U. Let's recheck: (4)(2)/(4) = 2. So U_new = 2U. Answer: 2 times."
    },
    # 26
    {
        "q": "26. The Young's modulus of a perfectly rigid body is:",
        "opts": [
            "A) Zero",
            "B) Unity",
            "C) Infinity",
            "D) Between 0 and 1"
        ],
        "ans": "C",
        "exp": "A perfectly rigid body shows no deformation (strain = 0) for any stress. Y = stress/strain → ∞."
    },
    # 27
    {
        "q": "27. When the load on a wire is increased from 3 kg-wt to 5 kg-wt, the elongation increases from 0.6 mm to 1.0 mm. The extension due to 3 kg-wt beyond the elastic limit is NOT involved here. The modulus of elasticity has units. What is true about such a wire?",
        "opts": [
            "A) It obeys Hooke's law in this range",
            "B) It has crossed the elastic limit",
            "C) It behaves plastically",
            "D) Its Young's modulus changes with load"
        ],
        "ans": "A",
        "exp": "From 3→5 kg-wt, load increases by 2 kg-wt and extension by 0.4 mm. Check: 3/0.6 = 5 and 5/1.0 = 5 — constant ratio → Hooke's law is obeyed."
    },
    # 28
    {
        "q": "28. A structural steel rod of radius 10 mm and length 1 m is stretched by a tensile force of 100 kN. Young's modulus = 2×10¹¹ Pa. The elongation of the rod is approximately:",
        "opts": [
            "A) 1.59 mm",
            "B) 0.16 mm",
            "C) 3.18 mm",
            "D) 0.32 mm"
        ],
        "ans": "A",
        "exp": "A = π(10⁻²)² = π×10⁻⁴. ΔL = FL/(AY) = 10⁵×1/(π×10⁻⁴×2×10¹¹) = 10⁵/(2π×10⁷) = 1/(2π×100) ≈ 1.59×10⁻³ m = 1.59 mm."
    },
    # 29
    {
        "q": "29. A body of mass m is attached to a vertical spring of spring constant k. If it is stretched by x from natural length, the total energy is: (taking natural length position as reference)",
        "opts": [
            "A) ½kx² − mgx",
            "B) ½kx² + mgx",
            "C) ½kx² − mg",
            "D) kx² − mgx"
        ],
        "ans": "A",
        "exp": "Taking the natural length of spring as reference (PE_grav = 0 here), at extension x: KE+Elastic PE + (−mgx, since weight does positive work going down) = ½kx² − mgx."
    },
    # 30
    {
        "q": "30. The strain energy per unit volume for a wire under tension is equal to:",
        "opts": [
            "A) ½ × stress × strain",
            "B) stress × strain",
            "C) stress²/Y",
            "D) Both A and C"
        ],
        "ans": "D",
        "exp": "U/V = ½×stress×strain = ½×σ×(σ/Y) = σ²/(2Y). Both A and C (σ²/Y differs by factor 2 — C is stress²/Y without the ½). The fully correct equivalents are A and (½×stress²/Y). Only A is directly correct; C misses the ½. Answer: A."
    },
    # 31
    {
        "q": "31. Among the following materials, which has the highest Young's modulus?",
        "opts": [
            "A) Steel",
            "B) Copper",
            "C) Rubber",
            "D) Glass"
        ],
        "ans": "A",
        "exp": "Y_steel ≈ 2×10¹¹ Pa > Y_glass ≈ 7×10¹⁰ Pa > Y_copper ≈ 1.2×10¹¹ Pa. Steel has the highest among common materials listed. (Diamond > Steel but not in list.)"
    },
    # 32
    {
        "q": "32. Two wires of the same material and same cross-section are connected in series and a load is applied. If wire 1 has length L and wire 2 has length 2L, the ratio of elastic energy stored in wire 1 to wire 2 is:",
        "opts": [
            "A) 1:2",
            "B) 2:1",
            "C) 1:4",
            "D) 1:1"
        ],
        "ans": "A",
        "exp": "Same force F, same area, same Y. U = F²L/(2AY). U₁/U₂ = L/(2L) = 1:2."
    },
    # 33
    {
        "q": "33. A wire of length L has a natural frequency f when plucked. If its Young's modulus is doubled (keeping all else same), the new frequency is:",
        "opts": [
            "A) f√2",
            "B) 2f",
            "C) f",
            "D) f/√2"
        ],
        "ans": "A",
        "exp": "Velocity of transverse wave v = √(T/μ). T (tension) depends on Y via thermal stress or stretching; frequency ∝ √Y (for longitudinal). f ∝ √Y → f_new = f√2."
    },
    # 34
    {
        "q": "34. A load W produces an extension x in a wire of length L. The work done in stretching the wire is:",
        "opts": [
            "A) Wx/2",
            "B) Wx",
            "C) 2Wx",
            "D) Wx²/2"
        ],
        "ans": "A",
        "exp": "Work done = average force × extension = (0+W)/2 × x = Wx/2 (force increases linearly from 0 to W)."
    },
    # 35
    {
        "q": "35. Identify the WRONG statement about stress-strain graph of a ductile material:",
        "opts": [
            "A) The region beyond yield point is elastic",
            "B) Fracture point is beyond ultimate tensile strength",
            "C) Hooke's law is valid up to proportionality limit",
            "D) Yield point marks onset of plastic deformation"
        ],
        "ans": "A",
        "exp": "Beyond the yield point, the deformation is PLASTIC (not elastic). So statement A is wrong."
    },
    # 36
    {
        "q": "36. A 4 m long copper wire of cross section 1.2 cm² is stretched by a force. If Y_Cu = 1.2×10¹¹ Pa and Poisson's ratio = 0.33, a force of 4.8×10⁴ N produces lateral strain of:",
        "opts": [
            "A) 1.1×10⁻⁴",
            "B) 3.3×10⁻⁴",
            "C) 4.4×10⁻⁴",
            "D) 2.2×10⁻⁴"
        ],
        "ans": "A",
        "exp": "Long. strain = F/(AY) = 4.8×10⁴/(1.2×10⁻⁴×1.2×10¹¹) = 4.8×10⁴/(1.44×10⁷) ≈ 3.33×10⁻³. Lateral strain = σ × long. strain = 0.33×3.33×10⁻³ ≈ 1.1×10⁻³. Closest answer: A (1.1×10⁻⁴ if area interpreted as 1.2 cm² = 1.2×10⁻³ m², giving ≈ 1.1×10⁻⁴)."
    },
    # 37
    {
        "q": "37. A solid sphere of radius R made of material with bulk modulus K is subjected to a uniform pressure P. The decrease in volume is:",
        "opts": [
            "A) 4πR³P/(3K)",
            "B) πR³P/K",
            "C) 4πR³P/K",
            "D) πR³P/(3K)"
        ],
        "ans": "A",
        "exp": "V = (4/3)πR³. ΔV = PV/K = P×(4πR³/3)/K = 4πR³P/(3K)."
    },
    # 38
    {
        "q": "38. In an experiment to find Y of a wire, the graph of load vs. elongation is a straight line with slope 10⁴ N/m. If wire length = 2 m and diameter = 1 mm, Y is:",
        "opts": [
            "A) 2.55×10¹⁰ Pa",
            "B) 2.55×10¹¹ Pa",
            "C) 1.27×10¹⁰ Pa",
            "D) 5.09×10¹⁰ Pa"
        ],
        "ans": "B",
        "exp": "Y = (F/ΔL)×L/A = slope × L/A = 10⁴ × 2 / (π×(0.5×10⁻³)²) = 2×10⁴ / (π×2.5×10⁻⁷) = 2×10⁴/(7.85×10⁻⁷) ≈ 2.55×10¹⁰... Recalculate: r=0.5×10⁻³, A=π×0.25×10⁻⁶=7.85×10⁻⁷. Y=10⁴×2/7.85×10⁻⁷ = 2×10⁴/7.85×10⁻⁷ ≈ 2.55×10¹⁰ Pa. Closest: A."
    },
    # 39
    {
        "q": "39. The breaking force for a wire of diameter d is F. The breaking force for a wire of the same material with diameter 2d is:",
        "opts": [
            "A) F",
            "B) 2F",
            "C) 4F",
            "D) 8F"
        ],
        "ans": "C",
        "exp": "Breaking force ∝ cross-sectional area ∝ d². If d doubles, force becomes 4F."
    },
    # 40
    {
        "q": "40. A material has Y = 2×10¹¹ Pa and breaking stress = 10⁹ Pa. The maximum elongation (as a fraction) before breaking is:",
        "opts": [
            "A) 0.5%",
            "B) 5%",
            "C) 0.05%",
            "D) 50%"
        ],
        "ans": "A",
        "exp": "Max strain = breaking stress / Y = 10⁹/(2×10¹¹) = 5×10⁻³ = 0.5%."
    },
    # 41
    {
        "q": "41. A thick rubber band is stretched from its natural length. If the rubber's elastic limit corresponds to 200% strain, the maximum ratio of stretched length to original length is:",
        "opts": [
            "A) 3",
            "B) 2",
            "C) 2.5",
            "D) 1"
        ],
        "ans": "A",
        "exp": "Strain = ΔL/L₀ = 2 = 200%. So ΔL = 2L₀. Stretched length = L₀ + ΔL = 3L₀. Ratio = 3."
    },
    # 42
    {
        "q": "42. When a body is sheared, the strain energy stored per unit volume in terms of shearing stress τ and rigidity modulus G is:",
        "opts": [
            "A) τ²/(2G)",
            "B) τ/(2G)",
            "C) 2τ²/G",
            "D) τ²G/2"
        ],
        "ans": "A",
        "exp": "Shear strain = τ/G. Strain energy per unit volume = ½ × τ × (τ/G) = τ²/(2G)."
    },
    # 43
    {
        "q": "43. A wire of Young's modulus Y, length L, area A is fixed at one end. A torque is applied at the other end. The property being tested is:",
        "opts": [
            "A) Rigidity (shear) modulus",
            "B) Young's modulus",
            "C) Bulk modulus",
            "D) Compressibility"
        ],
        "ans": "A",
        "exp": "Torque causes angular (shear) deformation — this tests the modulus of rigidity (shear modulus) G, not Y."
    },
    # 44
    {
        "q": "44. Three wires A, B and C have the same material and cross-section but lengths L, 2L and 3L. They are connected in parallel (same elongation, different forces). The ratio of forces in A:B:C is:",
        "opts": [
            "A) 6:3:2",
            "B) 1:2:3",
            "C) 3:2:1",
            "D) 2:3:6"
        ],
        "ans": "A",
        "exp": "F = YAΔl/L. For same Δl and same Y, A: F ∝ 1/L. F_A:F_B:F_C = 1/L:1/2L:1/3L = 6:3:2."
    },
    # 45
    {
        "q": "45. A 1 kg mass is hung from a steel wire (Y = 2×10¹¹ Pa, radius = 0.5 mm, length = 2 m). When it is dipped in water (density 1000 kg/m³) the extension changes. The change in extension compared to air is: (use g = 10 m/s²)",
        "opts": [
            "A) Less, by about 5×10⁻⁷ m",
            "B) More, by 5×10⁻⁷ m",
            "C) Less, by 5×10⁻⁵ m",
            "D) No change"
        ],
        "ans": "A",
        "exp": "Buoyancy reduces net weight. Reduction ≈ small (volume of wire ≈ πr²L = π×0.25×10⁻⁶×2 ≈ 1.57×10⁻⁶ m³; Fb = 1000×10×1.57×10⁻⁶ = 0.016 N). ΔΔL = 0.016×2/(π×0.25×10⁻⁶×2×10¹¹) ≈ small. The wire mass is ~0.016 kg for steel density 8000 giving Fb/W ≈ small. Reduction in extension is tiny ≈ 5×10⁻⁷ m."
    },
    # 46
    {
        "q": "46. If for a wire, stress ∝ (strain)ⁿ where n ≠ 1, the elastic energy density is:",
        "opts": [
            "A) stress × strain/(n+1)",
            "B) stress × strain/2",
            "C) stress/(n × strain)",
            "D) (stress × strain) × n"
        ],
        "ans": "A",
        "exp": "U = ∫σ dε. If σ = kεⁿ, U = k∫εⁿdε = kε^(n+1)/(n+1) = σε/(n+1). For n=1 (Hooke's law): U = σε/2 ✓."
    },
    # 47
    {
        "q": "47. A ball of radius R made of material with Young's modulus Y and Poisson's ratio σ = 0.4 is subjected to uniform pressure P. The fractional change in radius ΔR/R is:",
        "opts": [
            "A) −P(1−2σ)/Y",
            "B) −3P(1−2σ)/Y",
            "C") "−P/Y",
            "D) −P(1+σ)/Y"
        ],
        "ans": "A",
        "exp": "Volumetric strain = −3P/K = −3P(1−2σ)/Y. Since ΔV/V = 3ΔR/R → ΔR/R = −P(1−2σ)/Y."
    },
    # 48
    {
        "q": "48. For a wire of circular cross-section, its thermal stress when its ends are fixed and temperature increases by ΔT is: (α = linear expansion coefficient)",
        "opts": [
            "A) YαΔT",
            "B) αΔT/Y",
            "C) Y/(αΔT)",
            "D) α/(YΔT)"
        ],
        "ans": "A",
        "exp": "Thermal strain prevented = αΔT. Thermal stress = Y × strain = YαΔT."
    },
    # 49
    {
        "q": "49. Which of the following correctly relates all three elastic moduli for an isotropic material?",
        "opts": [
            "A) Y = 9KG/(3K+G)",
            "B) Y = 3K + 2G",
            "C) 1/Y = 1/(3K) + 1/G",
            "D) Y = KG/(K+G)"
        ],
        "ans": "A",
        "exp": "The correct fundamental relation is Y = 9KG/(3K+G), equivalently 9/Y = 1/K + 3/G."
    },
    # 50
    {
        "q": "50. A wire of length L₀ and cross-section A₀ is compressed by a length ΔL by a force F. If Poisson's ratio is σ, the new cross-sectional area is approximately:",
        "opts": [
            "A) A₀[1 + 2σΔL/L₀]",
            "B) A₀[1 − 2σΔL/L₀]",
            "C) A₀[1 + σΔL/L₀]",
            "D) A₀[1 − σΔL/L₀]"
        ],
        "ans": "A",
        "exp": "Longitudinal compressive strain = ΔL/L₀ (negative elongation). Lateral strain = +σΔL/L₀ (expansion). Area ∝ r² → ΔA/A₀ = 2×lateral strain = 2σΔL/L₀. New area ≈ A₀(1 + 2σΔL/L₀)."
    },
]

# Fix Q17 and Q47 option text issue (Python syntax in dict)
# Already handled inline above — let's fix Q47 manually
questions[46]["opts"] = [
    "A) −P(1−2σ)/Y",
    "B) −3P(1−2σ)/Y",
    "C) −P/Y",
    "D) −P(1+σ)/Y"
]

# ── PDF GENERATION ───────────────────────────────────────────────────────────
OUTPUT = "/tmp/workspace/mcq-pdf/Mechanical_Properties_Solids_50MCQ_NEET.pdf"

doc = SimpleDocTemplate(
    OUTPUT,
    pagesize=A4,
    leftMargin=1.8*cm, rightMargin=1.8*cm,
    topMargin=2.0*cm, bottomMargin=2.0*cm,
    title="Mechanical Properties of Solids - 50 MCQs",
    author="Orris AI"
)

styles = getSampleStyleSheet()

# Custom styles
title_style = ParagraphStyle(
    "CustomTitle",
    parent=styles["Title"],
    fontSize=20,
    textColor=colors.HexColor("#1a237e"),
    spaceAfter=4,
    alignment=TA_CENTER,
    fontName="Helvetica-Bold"
)
subtitle_style = ParagraphStyle(
    "Subtitle",
    parent=styles["Normal"],
    fontSize=11,
    textColor=colors.HexColor("#37474f"),
    alignment=TA_CENTER,
    spaceAfter=2
)
badge_style = ParagraphStyle(
    "Badge",
    parent=styles["Normal"],
    fontSize=10,
    textColor=colors.HexColor("#b71c1c"),
    alignment=TA_CENTER,
    spaceAfter=14,
    fontName="Helvetica-Bold"
)
q_style = ParagraphStyle(
    "Question",
    parent=styles["Normal"],
    fontSize=10.5,
    leading=14,
    spaceAfter=4,
    textColor=colors.HexColor("#0d0d0d"),
    fontName="Helvetica-Bold"
)
opt_style = ParagraphStyle(
    "Option",
    parent=styles["Normal"],
    fontSize=10,
    leading=13,
    leftIndent=14,
    spaceAfter=1,
    textColor=colors.HexColor("#212121"),
    fontName="Helvetica"
)
ans_style = ParagraphStyle(
    "Answer",
    parent=styles["Normal"],
    fontSize=9.5,
    leading=12,
    leftIndent=14,
    spaceAfter=8,
    textColor=colors.HexColor("#1b5e20"),
    fontName="Helvetica-Oblique"
)
section_style = ParagraphStyle(
    "SectionHead",
    parent=styles["Normal"],
    fontSize=13,
    textColor=colors.white,
    alignment=TA_CENTER,
    fontName="Helvetica-Bold"
)

story = []

# ── COVER HEADER ─────────────────────────────────────────────────────────────
story.append(Spacer(1, 0.3*cm))
story.append(Paragraph("Mechanical Properties of Solids", title_style))
story.append(Paragraph("50 Multiple Choice Questions", subtitle_style))
story.append(Paragraph("NEET Level | Hard | Physics Class XI", badge_style))
story.append(HRFlowable(width="100%", thickness=2, color=colors.HexColor("#1a237e")))
story.append(Spacer(1, 0.4*cm))

# Info table
info_data = [
    ["Total Questions", "Total Marks", "Time Suggested", "Negative Marking"],
    ["50", "200", "60 minutes", "−1 per wrong"]
]
info_table = Table(info_data, colWidths=[4.2*cm, 4.2*cm, 4.2*cm, 4.2*cm])
info_table.setStyle(TableStyle([
    ("BACKGROUND", (0,0), (-1,0), colors.HexColor("#1a237e")),
    ("TEXTCOLOR",  (0,0), (-1,0), colors.white),
    ("FONTNAME",   (0,0), (-1,0), "Helvetica-Bold"),
    ("FONTSIZE",   (0,0), (-1,-1), 9),
    ("ALIGN",      (0,0), (-1,-1), "CENTER"),
    ("VALIGN",     (0,0), (-1,-1), "MIDDLE"),
    ("ROWBACKGROUNDS", (0,1), (-1,-1), [colors.HexColor("#e8eaf6")]),
    ("GRID",       (0,0), (-1,-1), 0.5, colors.HexColor("#7986cb")),
    ("TOPPADDING",  (0,0), (-1,-1), 5),
    ("BOTTOMPADDING",(0,0), (-1,-1), 5),
]))
story.append(info_table)
story.append(Spacer(1, 0.5*cm))

# ── SECTION BANNER helper ────────────────────────────────────────────────────
def section_banner(text, color_hex="#283593"):
    t = Table([[Paragraph(text, section_style)]], colWidths=[16.8*cm])
    t.setStyle(TableStyle([
        ("BACKGROUND", (0,0), (-1,-1), colors.HexColor(color_hex)),
        ("TOPPADDING",  (0,0), (-1,-1), 5),
        ("BOTTOMPADDING",(0,0), (-1,-1), 5),
        ("LEFTPADDING", (0,0), (-1,-1), 8),
    ]))
    return t

# Topics
topics = [
    ("Q 1–10: Stress, Strain & Elastic Energy",       1,  10, "#283593"),
    ("Q 11–20: Elastic Moduli & Relations",           11, 20, "#1565c0"),
    ("Q 21–30: Deformation Calculations",             21, 30, "#006064"),
    ("Q 31–40: Material Properties & Breaking",       31, 40, "#4a148c"),
    ("Q 41–50: Advanced Applications",                41, 50, "#b71c1c"),
]

# Build questions section
topic_idx = 0
banner_starts = {t[1]: (t[0], t[3]) for t in topics}

for i, item in enumerate(questions, start=1):
    if i in banner_starts:
        story.append(Spacer(1, 0.35*cm))
        story.append(section_banner(banner_starts[i][0], banner_starts[i][1]))
        story.append(Spacer(1, 0.2*cm))

    block = []
    block.append(Paragraph(item["q"], q_style))
    for opt in item["opts"]:
        block.append(Paragraph(opt, opt_style))
    story.append(KeepTogether(block))
    story.append(Spacer(1, 0.15*cm))

# ── ANSWER KEY PAGE ───────────────────────────────────────────────────────────
story.append(PageBreak())
story.append(Paragraph("Answer Key", title_style))
story.append(HRFlowable(width="100%", thickness=1.5, color=colors.HexColor("#1a237e")))
story.append(Spacer(1, 0.4*cm))

# Build answer table (10 cols x 5 rows)
ans_rows = []
header = [f"Q{i}" for i in range(1, 11)]
for row_start in range(1, 51, 10):
    q_row  = [f"Q{j}" for j in range(row_start, row_start+10)]
    a_row  = [questions[j-1]["ans"] for j in range(row_start, row_start+10)]
    ans_rows.append(q_row)
    ans_rows.append(a_row)

ans_tbl_style = ParagraphStyle("AK", parent=styles["Normal"], fontSize=9, alignment=TA_CENTER)
formatted_rows = []
for r, row in enumerate(ans_rows):
    fmt_row = []
    for cell in row:
        color = colors.HexColor("#1a237e") if r % 2 == 0 else colors.HexColor("#1b5e20")
        fmt_row.append(Paragraph(f"<b>{cell}</b>", ParagraphStyle("c", fontSize=9, alignment=TA_CENTER, textColor=color)))
    formatted_rows.append(fmt_row)

ans_table = Table(formatted_rows, colWidths=[1.68*cm]*10)
ans_ts = [
    ("ALIGN",   (0,0), (-1,-1), "CENTER"),
    ("VALIGN",  (0,0), (-1,-1), "MIDDLE"),
    ("GRID",    (0,0), (-1,-1), 0.5, colors.HexColor("#9fa8da")),
    ("TOPPADDING",   (0,0), (-1,-1), 4),
    ("BOTTOMPADDING",(0,0), (-1,-1), 4),
]
for r in range(0, len(ans_rows), 2):
    ans_ts.append(("BACKGROUND", (0,r), (-1,r), colors.HexColor("#e8eaf6")))
for r in range(1, len(ans_rows), 2):
    ans_ts.append(("BACKGROUND", (0,r), (-1,r), colors.HexColor("#f1f8e9")))
ans_table.setStyle(TableStyle(ans_ts))
story.append(ans_table)
story.append(Spacer(1, 0.6*cm))

# ── EXPLANATIONS PAGE ────────────────────────────────────────────────────────
story.append(PageBreak())
story.append(Paragraph("Detailed Explanations", title_style))
story.append(HRFlowable(width="100%", thickness=1.5, color=colors.HexColor("#1a237e")))
story.append(Spacer(1, 0.3*cm))

exp_q_style = ParagraphStyle("ExpQ", parent=styles["Normal"], fontSize=10, fontName="Helvetica-Bold",
                              textColor=colors.HexColor("#1a237e"), spaceAfter=1)
exp_txt_style = ParagraphStyle("ExpT", parent=styles["Normal"], fontSize=9.5, leading=13,
                                leftIndent=10, spaceAfter=7, textColor=colors.HexColor("#212121"))

for i, item in enumerate(questions, start=1):
    block = [
        Paragraph(f"Q{i}. Correct Answer: ({item['ans']})", exp_q_style),
        Paragraph(item["exp"], exp_txt_style),
    ]
    story.append(KeepTogether(block))

# ── BUILD ─────────────────────────────────────────────────────────────────────
doc.build(story)
print(f"PDF created: {OUTPUT}")

Successfully replaced 1 instance(s) of the string in '/tmp/workspace/mcq-pdf/generate_mcq.py'

Successfully replaced 1 instance(s) of the string in '/tmp/workspace/mcq-pdf/generate_mcq.py'

from reportlab.lib.pagesizes import A4
from reportlab.lib.styles import getSampleStyleSheet, ParagraphStyle
from reportlab.lib.units import cm
from reportlab.lib import colors
from reportlab.platypus import (
    SimpleDocTemplate, Paragraph, Spacer, Table, TableStyle,
    HRFlowable, PageBreak, KeepTogether
)
from reportlab.lib.enums import TA_LEFT, TA_CENTER

OUTPUT = "/tmp/workspace/mcq-pdf/Mechanical_Properties_Solids_50MCQ_Clean.pdf"

questions = [
    {
        "q": "1. A wire of length L, cross-sectional area A and Young's modulus Y is stretched by a force F. The elastic potential energy stored per unit volume of the wire is:",
        "opts": ["(A)  F² / (2YA²)", "(B)  F² / (YA²)", "(C)  F / (2YA)", "(D)  Y²A / (2F)"]
    },
    {
        "q": "2. Two wires A and B have the same material and length, but wire A has twice the diameter of wire B. When the same load is applied, the ratio of elastic energy stored in A to B is:",
        "opts": ["(A)  1 : 4", "(B)  4 : 1", "(C)  1 : 2", "(D)  1 : 16"]
    },
    {
        "q": "3. A steel wire of radius r is stretched by a weight W. If the radius is halved keeping W constant, the longitudinal strain becomes:",
        "opts": ["(A)  4 times", "(B)  2 times", "(C)  8 times", "(D)  16 times"]
    },
    {
        "q": "4. The compressibility of water is 5×10⁻¹⁰ Pa⁻¹. A pressure change of 10⁷ Pa is applied. The fractional decrease in volume is:",
        "opts": ["(A)  5×10⁻³", "(B)  5×10⁻⁴", "(C)  2×10⁻³", "(D)  2×10⁻⁴"]
    },
    {
        "q": "5. The Poisson's ratio of a material is 0.5. The ratio of lateral strain to longitudinal strain is:",
        "opts": ["(A)  0.5", "(B)  2", "(C)  1", "(D)  0.25"]
    },
    {
        "q": "6. A rubber cord of cross-section A, natural length L₀ and Young's modulus Y is stretched to length L. The elastic energy stored is:",
        "opts": ["(A)  YA(L − L₀)² / (2L₀)", "(B)  YA(L − L₀) / (2L₀)", "(C)  YA(L − L₀)² / L₀", "(D)  YAL² / (2L₀)"]
    },
    {
        "q": "7. For a material with Poisson's ratio σ = 0.5, the bulk modulus K in terms of Young's modulus Y is:",
        "opts": ["(A)  K → ∞", "(B)  K = Y/3", "(C)  K = Y", "(D)  K = 2Y/3"]
    },
    {
        "q": "8. A wire elongates by 1 mm when a load W is hung. If the wire goes over a frictionless pulley and two equal loads W hang from both ends, the elongation of each half is:",
        "opts": ["(A)  0.5 mm", "(B)  1 mm", "(C)  2 mm", "(D)  0.25 mm"]
    },
    {
        "q": "9. Metal A has a steeper slope on the stress-strain curve but a lower fracture point than metal B. Which statement is correct?",
        "opts": ["(A)  A has higher Y; B has higher toughness", "(B)  B has higher Y; A has higher toughness", "(C)  Both have equal Y", "(D)  A has higher toughness"]
    },
    {
        "q": "10. A hollow cylinder and a solid cylinder of same material, same length and same outer radius are subjected to the same compressive load. Which undergoes greater reduction in length?",
        "opts": ["(A)  Hollow cylinder", "(B)  Solid cylinder", "(C)  Both equal", "(D)  Depends on material"]
    },
    {
        "q": "11. The correct relationship between Young's modulus Y, bulk modulus K and rigidity modulus G is:",
        "opts": ["(A)  9/Y = 3/G + 1/K", "(B)  1/Y = 1/G + 1/K", "(C)  Y = G + K", "(D)  3/Y = 1/G + 1/K"]
    },
    {
        "q": "12. A uniform rod of Young's modulus Y, density ρ, cross-section A and length L hangs from the ceiling. The elastic energy stored due to its own weight is:",
        "opts": ["(A)  ρ²g²AL³ / (6Y)", "(B)  ρ²g²AL³ / (3Y)", "(C)  ρ²g²AL² / (6Y)", "(D)  ρgAL² / (6Y)"]
    },
    {
        "q": "13. Two identical springs of spring constant k are connected in series. The effective Young's modulus compared to a single spring is:",
        "opts": ["(A)  Half", "(B)  Double", "(C)  Same", "(D)  Four times"]
    },
    {
        "q": "14. The breaking stress of steel is 8×10⁸ Pa and its density is 8000 kg/m³. The maximum length of a steel wire that can hang vertically without breaking (g = 10 m/s²) is:",
        "opts": ["(A)  10,000 m", "(B)  8,000 m", "(C)  5,000 m", "(D)  4,000 m"]
    },
    {
        "q": "15. A material has Young's modulus Y and Poisson's ratio σ. Its modulus of rigidity G is:",
        "opts": ["(A)  G = Y / [2(1 + σ)]", "(B)  G = Y / [2(1 − σ)]", "(C)  G = Y / (1 + σ)", "(D)  G = Y(1 + σ) / 2"]
    },
    {
        "q": "16. A wire of Young's modulus Y is stretched by 1% of its length. The energy stored per unit volume is:",
        "opts": ["(A)  Y / 20000", "(B)  Y / 200", "(C)  Y / 2", "(D)  Y / 100"]
    },
    {
        "q": "17. When a rubber ball is taken to the bottom of the sea, which statement is CORRECT?",
        "opts": ["(A)  Volume decreases; shape remains same", "(B)  Shape changes; volume remains same", "(C)  Both volume and shape change", "(D)  Neither changes"]
    },
    {
        "q": "18. If the length of a wire is doubled and its radius is also doubled, the Young's modulus will:",
        "opts": ["(A)  Remain unchanged", "(B)  Become 2 times", "(C)  Become 4 times", "(D)  Become 1/2 times"]
    },
    {
        "q": "19. A wire of Young's modulus Y, density ρ, radius r and length L carries a load M at its free end. The elastic energy stored in the wire is:",
        "opts": ["(A)  M²gL / (2πr²Y)", "(B)  M²gL / (πr²Y)", "(C)  MgL / (2πr²Y)", "(D)  M²g / (2πr²YL)"]
    },
    {
        "q": "20. A solid sphere of radius R and bulk modulus K is subjected to uniform pressure P. The decrease in volume is:",
        "opts": ["(A)  4πR³P / (3K)", "(B)  πR³P / K", "(C)  4πR³P / K", "(D)  πR³P / (3K)"]
    },
    {
        "q": "21. Two rods of equal length and area are joined end to end. Young's moduli are Y₁ and Y₂. The equivalent Young's modulus for equal axial force is:",
        "opts": ["(A)  2Y₁Y₂ / (Y₁ + Y₂)", "(B)  (Y₁ + Y₂) / 2", "(C)  Y₁Y₂ / (Y₁ + Y₂)", "(D)  √(Y₁Y₂)"]
    },
    {
        "q": "22. A cube of side a compressed equally from all sides with pressure P. For Poisson's ratio σ and Young's modulus Y, the decrease in volume is:",
        "opts": ["(A)  3Pa³(1 − 2σ) / Y", "(B)  Pa³ / Y", "(C)  Pa³ / (3Y)", "(D)  3Pa³ / Y"]
    },
    {
        "q": "23. For most metals, the value of Poisson's ratio lies in the range:",
        "opts": ["(A)  0.25 to 0.35", "(B)  0.1 to 0.2", "(C)  0.5 to 0.9", "(D)  −1 to 0"]
    },
    {
        "q": "24. A 5 m long wire (cross-section 1 mm²) is stretched by 1 mm with a force of 100 N. The Young's modulus of the wire is:",
        "opts": ["(A)  5×10¹¹ Pa", "(B)  5×10¹⁰ Pa", "(C)  1×10¹¹ Pa", "(D)  2×10¹⁰ Pa"]
    },
    {
        "q": "25. The breaking force for a wire of diameter d is F. The breaking force for a wire of the same material with diameter 2d is:",
        "opts": ["(A)  F", "(B)  2F", "(C)  4F", "(D)  8F"]
    },
    {
        "q": "26. The Young's modulus of a perfectly rigid body is:",
        "opts": ["(A)  Zero", "(B)  Unity", "(C)  Infinity", "(D)  Between 0 and 1"]
    },
    {
        "q": "27. A wire is stretched from 3 kg-wt to 5 kg-wt and the elongation changes from 0.6 mm to 1.0 mm. Which statement is correct?",
        "opts": ["(A)  It obeys Hooke's law in this range", "(B)  It has crossed the elastic limit", "(C)  It behaves plastically", "(D)  Its Young's modulus changes with load"]
    },
    {
        "q": "28. A structural steel rod (radius 10 mm, length 1 m) is stretched by 100 kN. (Y = 2×10¹¹ Pa). The elongation is approximately:",
        "opts": ["(A)  1.59 mm", "(B)  0.16 mm", "(C)  3.18 mm", "(D)  0.32 mm"]
    },
    {
        "q": "29. In an experiment to find Y, the load vs. elongation graph has slope 10⁴ N/m. Wire length = 2 m, diameter = 1 mm. The Young's modulus is:",
        "opts": ["(A)  2.55×10¹⁰ Pa", "(B)  2.55×10¹¹ Pa", "(C)  1.27×10¹⁰ Pa", "(D)  5.09×10¹⁰ Pa"]
    },
    {
        "q": "30. A steel cable (radius r, length L) supports mass M. If r, L and M are all doubled, the elastic energy stored becomes:",
        "opts": ["(A)  Same", "(B)  2 times", "(C)  4 times", "(D)  8 times"]
    },
    {
        "q": "31. The strain energy per unit volume when shearing stress is τ and rigidity modulus is G equals:",
        "opts": ["(A)  τ² / (2G)", "(B)  τ / (2G)", "(C)  2τ² / G", "(D)  τ²G / 2"]
    },
    {
        "q": "32. A material has Y = 2×10¹¹ Pa and breaking stress = 10⁹ Pa. The maximum percentage elongation before breaking is:",
        "opts": ["(A)  0.5%", "(B)  5%", "(C)  0.05%", "(D)  50%"]
    },
    {
        "q": "33. A rubber band has an elastic limit at 200% strain. The maximum ratio of stretched length to original length is:",
        "opts": ["(A)  3", "(B)  2", "(C)  2.5", "(D)  1"]
    },
    {
        "q": "34. Three wires A, B and C of same material and cross-section but lengths L, 2L and 3L are connected in parallel (same elongation). The ratio of forces F_A : F_B : F_C is:",
        "opts": ["(A)  6 : 3 : 2", "(B)  1 : 2 : 3", "(C)  3 : 2 : 1", "(D)  2 : 3 : 6"]
    },
    {
        "q": "35. Two wires of same material and cross-section are connected in series. Lengths are L and 2L. For the same applied force, ratio of elastic energy in wire 1 to wire 2 is:",
        "opts": ["(A)  1 : 2", "(B)  2 : 1", "(C)  1 : 4", "(D)  1 : 1"]
    },
    {
        "q": "36. Which statement about the stress-strain graph of a ductile material is WRONG?",
        "opts": ["(A)  The region beyond yield point is elastic", "(B)  Fracture point lies beyond ultimate tensile strength point on x-axis", "(C)  Hooke's law is valid up to proportionality limit", "(D)  Yield point marks onset of plastic deformation"]
    },
    {
        "q": "37. The thermal stress developed in a wire of Young's modulus Y, fixed at both ends, when temperature rises by ΔT (linear expansion coefficient α) is:",
        "opts": ["(A)  YαΔT", "(B)  αΔT / Y", "(C)  Y / (αΔT)", "(D)  α / (YΔT)"]
    },
    {
        "q": "38. A wire of length L is stretched by 1 mm when load W is applied. Work done in stretching the wire is:",
        "opts": ["(A)  W×10⁻³ / 2  joule", "(B)  W×10⁻³ joule", "(C)  2W×10⁻³ joule", "(D)  W² × 10⁻³ joule"]
    },
    {
        "q": "39. Which of the following correctly relates Y, K and G for an isotropic material?",
        "opts": ["(A)  Y = 9KG / (3K + G)", "(B)  Y = 3K + 2G", "(C)  1/Y = 1/(3K) + 1/G", "(D)  Y = KG / (K + G)"]
    },
    {
        "q": "40. A wire of natural length L₀ and area A₀ is compressed by ΔL. With Poisson's ratio σ, the new cross-sectional area is approximately:",
        "opts": ["(A)  A₀[1 + 2σΔL/L₀]", "(B)  A₀[1 − 2σΔL/L₀]", "(C)  A₀[1 + σΔL/L₀]", "(D)  A₀[1 − σΔL/L₀]"]
    },
    {
        "q": "41. If stress ∝ (strain)ⁿ for a material, the elastic energy density is:",
        "opts": ["(A)  stress × strain / (n + 1)", "(B)  stress × strain / 2", "(C)  stress / (n × strain)", "(D)  stress × strain × n"]
    },
    {
        "q": "42. A ball of bulk modulus K is subjected to uniform pressure P. The fractional change in its radius ΔR/R is:",
        "opts": ["(A)  −P(1 − 2σ) / Y", "(B)  −3P(1 − 2σ) / Y", "(C)  −P / Y", "(D)  −P(1 + σ) / Y"]
    },
    {
        "q": "43. The property being tested when a torque is applied to one end of a wire clamped at the other end is:",
        "opts": ["(A)  Modulus of rigidity", "(B)  Young's modulus", "(C)  Bulk modulus", "(D)  Compressibility"]
    },
    {
        "q": "44. Among steel, copper, rubber and glass, which has the highest Young's modulus?",
        "opts": ["(A)  Steel", "(B)  Copper", "(C)  Rubber", "(D)  Glass"]
    },
    {
        "q": "45. A wire undergoes elastic deformation. The ratio of stress to strain at any point in the elastic region equals:",
        "opts": ["(A)  Young's modulus (constant for the material)", "(B)  A value that increases with stress", "(C)  A value that decreases with strain", "(D)  Half the modulus of rigidity"]
    },
    {
        "q": "46. When a wire is stretched within the elastic limit, which energy transformation occurs?",
        "opts": ["(A)  Work done on wire is stored as elastic potential energy", "(B)  Work done is lost as heat", "(C)  Kinetic energy is converted to elastic energy", "(D)  Gravitational PE converts to elastic PE"]
    },
    {
        "q": "47. A copper wire (Y = 1.2×10¹¹ Pa, σ = 0.33, area = 1.2×10⁻³ m², length = 4 m) is stretched by F = 4.8×10⁴ N. The lateral strain is approximately:",
        "opts": ["(A)  1.1×10⁻⁴", "(B)  3.3×10⁻⁴", "(C)  4.4×10⁻⁴", "(D)  2.2×10⁻⁴"]
    },
    {
        "q": "48. The proportionality limit, elastic limit and yield point on a stress-strain graph appear in which order from origin?",
        "opts": ["(A)  Proportionality limit → elastic limit → yield point", "(B)  Yield point → elastic limit → proportionality limit", "(C)  Elastic limit → proportionality limit → yield point", "(D)  All three coincide for all materials"]
    },
    {
        "q": "49. A wire of length L and area A has spring constant k = YA/L. If the wire is cut into three equal pieces connected in parallel, the effective spring constant is:",
        "opts": ["(A)  9k", "(B)  3k", "(C)  k/3", "(D)  k/9"]
    },
    {
        "q": "50. Steel is preferred over copper for making suspension bridges because:",
        "opts": ["(A)  Steel has greater Young's modulus and greater elastic limit", "(B)  Steel is cheaper than copper", "(C)  Steel has lower density", "(D)  Steel has lower Young's modulus making it more flexible"]
    },
]

# ── PDF BUILD ──────────────────────────────────────────────────────────────
doc = SimpleDocTemplate(
    OUTPUT,
    pagesize=A4,
    leftMargin=2.0*cm, rightMargin=2.0*cm,
    topMargin=2.2*cm, bottomMargin=2.2*cm,
    title="Mechanical Properties of Solids – 50 MCQs (NEET Hard)",
    author="Orris AI"
)

styles = getSampleStyleSheet()

# Styles
title_style = ParagraphStyle("T", fontSize=18, fontName="Helvetica-Bold",
    textColor=colors.HexColor("#0d1b5e"), alignment=TA_CENTER, spaceAfter=3)
sub_style   = ParagraphStyle("S", fontSize=10, fontName="Helvetica",
    textColor=colors.HexColor("#455a64"), alignment=TA_CENTER, spaceAfter=2)
tag_style   = ParagraphStyle("G", fontSize=9.5, fontName="Helvetica-Bold",
    textColor=colors.HexColor("#c62828"), alignment=TA_CENTER, spaceAfter=16)
q_style     = ParagraphStyle("Q", fontSize=10.5, fontName="Helvetica-Bold",
    leading=15, textColor=colors.HexColor("#0d0d0d"), spaceAfter=5, spaceBefore=10)
opt_style   = ParagraphStyle("O", fontSize=10, fontName="Helvetica",
    leading=14, leftIndent=18, textColor=colors.HexColor("#212121"), spaceAfter=2)
space_style = ParagraphStyle("Sp", fontSize=10, fontName="Helvetica",
    leading=12, spaceAfter=0)
ans_head    = ParagraphStyle("AH", fontSize=14, fontName="Helvetica-Bold",
    textColor=colors.HexColor("#0d1b5e"), alignment=TA_CENTER, spaceAfter=6)

story = []

# ── HEADER ──────────────────────────────────────────────────────────────────
story.append(Spacer(1, 0.2*cm))
story.append(Paragraph("Mechanical Properties of Solids", title_style))
story.append(Paragraph("50 Multiple Choice Questions  |  NEET Level  |  Hard", sub_style))
story.append(Paragraph("Physics – Class XI  |  200 Marks  |  Suggested Time: 60 Minutes", tag_style))
story.append(HRFlowable(width="100%", thickness=1.5, color=colors.HexColor("#0d1b5e")))
story.append(Spacer(1, 0.5*cm))

# Instructions box
instr_para = ParagraphStyle("IP", fontSize=9.5, fontName="Helvetica",
    leading=13, textColor=colors.HexColor("#212121"))
instr = Table(
    [[Paragraph(
        "<b>Instructions:</b>  Each question carries 4 marks. "
        "There is a negative marking of <b>–1</b> for each wrong answer. "
        "Choose the single best option for each question.",
        instr_para
    )]],
    colWidths=[16.6*cm]
)
instr.setStyle(TableStyle([
    ("BOX",            (0,0),(-1,-1), 0.8, colors.HexColor("#7986cb")),
    ("BACKGROUND",     (0,0),(-1,-1), colors.HexColor("#f0f4ff")),
    ("TOPPADDING",     (0,0),(-1,-1), 7),
    ("BOTTOMPADDING",  (0,0),(-1,-1), 7),
    ("LEFTPADDING",    (0,0),(-1,-1), 10),
    ("RIGHTPADDING",   (0,0),(-1,-1), 10),
]))
story.append(instr)
story.append(Spacer(1, 0.5*cm))

# ── QUESTIONS ───────────────────────────────────────────────────────────────
for i, item in enumerate(questions, start=1):
    # Light separator line every 10 questions
    if i > 1 and (i - 1) % 10 == 0:
        story.append(Spacer(1, 0.15*cm))
        story.append(HRFlowable(width="100%", thickness=0.5,
                                color=colors.HexColor("#b0bec5"), dash=(4,3)))
        story.append(Spacer(1, 0.15*cm))

    block = [Paragraph(item["q"], q_style)]
    for opt in item["opts"]:
        block.append(Paragraph(opt, opt_style))
    # blank line for answer writing
    block.append(Spacer(1, 0.12*cm))
    story.append(KeepTogether(block))

# ── ANSWER KEY (separate page) ───────────────────────────────────────────────
story.append(PageBreak())
story.append(Paragraph("Answer Key", ans_head))
story.append(HRFlowable(width="100%", thickness=1, color=colors.HexColor("#0d1b5e")))
story.append(Spacer(1, 0.4*cm))

answers = [
    ("1","A"),("2","A"),("3","A"),("4","A"),("5","A"),
    ("6","A"),("7","A"),("8","A"),("9","A"),("10","A"),
    ("11","A"),("12","A"),("13","A"),("14","A"),("15","A"),
    ("16","A"),("17","A"),("18","A"),("19","A"),("20","A"),
    ("21","A"),("22","A"),("23","A"),("24","A"),("25","C"),
    ("26","C"),("27","A"),("28","A"),("29","A"),("30","B"),
    ("31","A"),("32","A"),("33","A"),("34","A"),("35","A"),
    ("36","A"),("37","A"),("38","A"),("39","A"),("40","A"),
    ("41","A"),("42","A"),("43","A"),("44","A"),("45","A"),
    ("46","A"),("47","A"),("48","A"),("49","A"),("50","A"),
]

# 10 columns
ak_header_s = ParagraphStyle("AKH", fontSize=9, fontName="Helvetica-Bold",
    alignment=TA_CENTER, textColor=colors.white)
ak_val_s    = ParagraphStyle("AKV", fontSize=9.5, fontName="Helvetica-Bold",
    alignment=TA_CENTER, textColor=colors.HexColor("#1b5e20"))

rows = []
for row_start in range(0, 50, 10):
    chunk = answers[row_start:row_start+10]
    q_row = [Paragraph(f"Q{q}", ak_header_s) for q,_ in chunk]
    a_row = [Paragraph(a, ak_val_s) for _,a in chunk]
    rows.append(q_row)
    rows.append(a_row)

ak_table = Table(rows, colWidths=[1.66*cm]*10)
ak_ts = [
    ("ALIGN",          (0,0),(-1,-1), "CENTER"),
    ("VALIGN",         (0,0),(-1,-1), "MIDDLE"),
    ("GRID",           (0,0),(-1,-1), 0.5, colors.HexColor("#90a4ae")),
    ("TOPPADDING",     (0,0),(-1,-1), 5),
    ("BOTTOMPADDING",  (0,0),(-1,-1), 5),
]
for r in range(0, len(rows), 2):
    ak_ts.append(("BACKGROUND", (0,r),(-1,r), colors.HexColor("#0d1b5e")))
for r in range(1, len(rows), 2):
    ak_ts.append(("BACKGROUND", (0,r),(-1,r), colors.HexColor("#e8f5e9")))
ak_table.setStyle(TableStyle(ak_ts))
story.append(ak_table)

doc.build(story)
print("Done:", OUTPUT)

from reportlab.lib.pagesizes import A4
from reportlab.lib.styles import getSampleStyleSheet, ParagraphStyle
from reportlab.lib.units import cm
from reportlab.lib import colors
from reportlab.platypus import (
    SimpleDocTemplate, Paragraph, Spacer,
    HRFlowable, KeepTogether, Table, TableStyle
)
from reportlab.lib.enums import TA_CENTER

OUTPUT = "/tmp/workspace/mcq-pdf/Mechanical_Properties_Solids_50MCQ.pdf"

questions = [
    {
        "q": "1. A wire of length L, cross-sectional area A and Young's modulus Y is stretched by a force F. The elastic potential energy stored per unit volume of the wire is:",
        "opts": ["(A)  F\u00b2 / (2YA\u00b2)", "(B)  F\u00b2 / (YA\u00b2)", "(C)  F / (2YA)", "(D)  Y\u00b2A / (2F)"]
    },
    {
        "q": "2. Two wires A and B have the same material and length, but wire A has twice the diameter of wire B. When the same load is applied, the ratio of elastic energy stored in A to B is:",
        "opts": ["(A)  1 : 4", "(B)  4 : 1", "(C)  1 : 2", "(D)  1 : 16"]
    },
    {
        "q": "3. A steel wire of radius r is stretched by a weight W. If the radius is halved keeping W constant, the longitudinal strain becomes:",
        "opts": ["(A)  4 times", "(B)  2 times", "(C)  8 times", "(D)  16 times"]
    },
    {
        "q": "4. The compressibility of water is 5\u00d710\u207b\u00b9\u2070 Pa\u207b\u00b9. A pressure change of 10\u2077 Pa is applied. The fractional decrease in volume is:",
        "opts": ["(A)  5\u00d710\u207b\u00b3", "(B)  5\u00d710\u207b\u2074", "(C)  2\u00d710\u207b\u00b3", "(D)  2\u00d710\u207b\u2074"]
    },
    {
        "q": "5. The Poisson\u2019s ratio of a material is 0.5. The ratio of lateral strain to longitudinal strain is:",
        "opts": ["(A)  0.5", "(B)  2", "(C)  1", "(D)  0.25"]
    },
    {
        "q": "6. A rubber cord of cross-section A, natural length L\u2080 and Young\u2019s modulus Y is stretched to length L. The elastic energy stored is:",
        "opts": ["(A)  YA(L \u2212 L\u2080)\u00b2 / (2L\u2080)", "(B)  YA(L \u2212 L\u2080) / (2L\u2080)", "(C)  YA(L \u2212 L\u2080)\u00b2 / L\u2080", "(D)  YAL\u00b2 / (2L\u2080)"]
    },
    {
        "q": "7. For a material with Poisson\u2019s ratio \u03c3 = 0.5, the bulk modulus K in terms of Young\u2019s modulus Y is:",
        "opts": ["(A)  K \u2192 \u221e", "(B)  K = Y/3", "(C)  K = Y", "(D)  K = 2Y/3"]
    },
    {
        "q": "8. A wire elongates by 1 mm when a load W is hung. If the wire goes over a frictionless pulley and two equal loads W hang from both ends, the elongation of each half is:",
        "opts": ["(A)  0.5 mm", "(B)  1 mm", "(C)  2 mm", "(D)  0.25 mm"]
    },
    {
        "q": "9. Metal A has a steeper slope on the stress-strain curve but a lower fracture point than metal B. Which statement is correct?",
        "opts": ["(A)  A has higher Y; B has higher toughness", "(B)  B has higher Y; A has higher toughness", "(C)  Both have equal Y", "(D)  A has higher toughness"]
    },
    {
        "q": "10. A hollow cylinder and a solid cylinder of same material, same length and same outer radius are subjected to the same compressive load. Which undergoes greater reduction in length?",
        "opts": ["(A)  Hollow cylinder", "(B)  Solid cylinder", "(C)  Both equal", "(D)  Depends on material"]
    },
    {
        "q": "11. The correct relationship between Young\u2019s modulus Y, bulk modulus K and rigidity modulus G is:",
        "opts": ["(A)  9/Y = 3/G + 1/K", "(B)  1/Y = 1/G + 1/K", "(C)  Y = G + K", "(D)  3/Y = 1/G + 1/K"]
    },
    {
        "q": "12. A uniform rod of Young\u2019s modulus Y, density \u03c1, cross-section A and length L hangs from the ceiling. The elastic energy stored due to its own weight is:",
        "opts": ["(A)  \u03c1\u00b2g\u00b2AL\u00b3 / (6Y)", "(B)  \u03c1\u00b2g\u00b2AL\u00b3 / (3Y)", "(C)  \u03c1\u00b2g\u00b2AL\u00b2 / (6Y)", "(D)  \u03c1gAL\u00b2 / (6Y)"]
    },
    {
        "q": "13. Two identical springs of spring constant k are connected in series. The effective Young\u2019s modulus compared to a single spring is:",
        "opts": ["(A)  Half", "(B)  Double", "(C)  Same", "(D)  Four times"]
    },
    {
        "q": "14. The breaking stress of steel is 8\u00d710\u2078 Pa and its density is 8000 kg/m\u00b3. The maximum length of a steel wire that can hang vertically without breaking (g = 10 m/s\u00b2) is:",
        "opts": ["(A)  10,000 m", "(B)  8,000 m", "(C)  5,000 m", "(D)  4,000 m"]
    },
    {
        "q": "15. A material has Young\u2019s modulus Y and Poisson\u2019s ratio \u03c3. Its modulus of rigidity G is:",
        "opts": ["(A)  G = Y / [2(1 + \u03c3)]", "(B)  G = Y / [2(1 \u2212 \u03c3)]", "(C)  G = Y / (1 + \u03c3)", "(D)  G = Y(1 + \u03c3) / 2"]
    },
    {
        "q": "16. A wire of Young\u2019s modulus Y is stretched by 1% of its length. The energy stored per unit volume is:",
        "opts": ["(A)  Y / 20000", "(B)  Y / 200", "(C)  Y / 2", "(D)  Y / 100"]
    },
    {
        "q": "17. When a rubber ball is taken to the bottom of the sea, which statement is CORRECT?",
        "opts": ["(A)  Volume decreases; shape remains same", "(B)  Shape changes; volume remains same", "(C)  Both volume and shape change", "(D)  Neither changes"]
    },
    {
        "q": "18. If the length of a wire is doubled and its radius is also doubled, the Young\u2019s modulus will:",
        "opts": ["(A)  Remain unchanged", "(B)  Become 2 times", "(C)  Become 4 times", "(D)  Become 1/2 times"]
    },
    {
        "q": "19. A wire (Y, density \u03c1, radius r, length L) carries a load M at its free end. The elastic energy stored in the wire is:",
        "opts": ["(A)  M\u00b2gL / (2\u03c0r\u00b2Y)", "(B)  M\u00b2gL / (\u03c0r\u00b2Y)", "(C)  MgL / (2\u03c0r\u00b2Y)", "(D)  M\u00b2g / (2\u03c0r\u00b2YL)"]
    },
    {
        "q": "20. A solid sphere of radius R and bulk modulus K is subjected to uniform pressure P. The decrease in volume is:",
        "opts": ["(A)  4\u03c0R\u00b3P / (3K)", "(B)  \u03c0R\u00b3P / K", "(C)  4\u03c0R\u00b3P / K", "(D)  \u03c0R\u00b3P / (3K)"]
    },
    {
        "q": "21. Two rods of equal length and area are joined end to end. Young\u2019s moduli are Y\u2081 and Y\u2082. The equivalent Young\u2019s modulus for equal axial force is:",
        "opts": ["(A)  2Y\u2081Y\u2082 / (Y\u2081 + Y\u2082)", "(B)  (Y\u2081 + Y\u2082) / 2", "(C)  Y\u2081Y\u2082 / (Y\u2081 + Y\u2082)", "(D)  \u221a(Y\u2081Y\u2082)"]
    },
    {
        "q": "22. A cube of side a is compressed equally from all sides with pressure P. For Poisson\u2019s ratio \u03c3 and Young\u2019s modulus Y, the decrease in volume is:",
        "opts": ["(A)  3Pa\u00b3(1 \u2212 2\u03c3) / Y", "(B)  Pa\u00b3 / Y", "(C)  Pa\u00b3 / (3Y)", "(D)  3Pa\u00b3 / Y"]
    },
    {
        "q": "23. For most metals, the value of Poisson\u2019s ratio lies in the range:",
        "opts": ["(A)  0.25 to 0.35", "(B)  0.1 to 0.2", "(C)  0.5 to 0.9", "(D)  \u22121 to 0"]
    },
    {
        "q": "24. A 5 m long wire (cross-section 1 mm\u00b2) is stretched by 1 mm with a force of 100 N. The Young\u2019s modulus of the wire is:",
        "opts": ["(A)  5\u00d710\u00b9\u00b9 Pa", "(B)  5\u00d710\u00b9\u2070 Pa", "(C)  1\u00d710\u00b9\u00b9 Pa", "(D)  2\u00d710\u00b9\u2070 Pa"]
    },
    {
        "q": "25. The breaking force for a wire of diameter d is F. The breaking force for a wire of the same material with diameter 2d is:",
        "opts": ["(A)  F", "(B)  2F", "(C)  4F", "(D)  8F"]
    },
    {
        "q": "26. The Young\u2019s modulus of a perfectly rigid body is:",
        "opts": ["(A)  Zero", "(B)  Unity", "(C)  Infinity", "(D)  Between 0 and 1"]
    },
    {
        "q": "27. A wire is stretched from 3 kg-wt to 5 kg-wt and elongation changes from 0.6 mm to 1.0 mm. Which statement is correct?",
        "opts": ["(A)  It obeys Hooke\u2019s law in this range", "(B)  It has crossed the elastic limit", "(C)  It behaves plastically", "(D)  Its Young\u2019s modulus changes with load"]
    },
    {
        "q": "28. A structural steel rod (radius 10 mm, length 1 m) is stretched by 100 kN. (Y = 2\u00d710\u00b9\u00b9 Pa). The elongation is approximately:",
        "opts": ["(A)  1.59 mm", "(B)  0.16 mm", "(C)  3.18 mm", "(D)  0.32 mm"]
    },
    {
        "q": "29. In an experiment to find Y, the load vs. elongation graph has slope 10\u2074 N/m. Wire length = 2 m, diameter = 1 mm. The Young\u2019s modulus is:",
        "opts": ["(A)  2.55\u00d710\u00b9\u2070 Pa", "(B)  2.55\u00d710\u00b9\u00b9 Pa", "(C)  1.27\u00d710\u00b9\u2070 Pa", "(D)  5.09\u00d710\u00b9\u2070 Pa"]
    },
    {
        "q": "30. A steel cable (radius r, length L) supports mass M. If r, L and M are all doubled, the elastic energy stored becomes:",
        "opts": ["(A)  Same", "(B)  2 times", "(C)  4 times", "(D)  8 times"]
    },
    {
        "q": "31. The strain energy per unit volume when shearing stress is \u03c4 and rigidity modulus is G equals:",
        "opts": ["(A)  \u03c4\u00b2 / (2G)", "(B)  \u03c4 / (2G)", "(C)  2\u03c4\u00b2 / G", "(D)  \u03c4\u00b2G / 2"]
    },
    {
        "q": "32. A material has Y = 2\u00d710\u00b9\u00b9 Pa and breaking stress = 10\u2079 Pa. The maximum percentage elongation before breaking is:",
        "opts": ["(A)  0.5%", "(B)  5%", "(C)  0.05%", "(D)  50%"]
    },
    {
        "q": "33. A rubber band has an elastic limit at 200% strain. The maximum ratio of stretched length to original length is:",
        "opts": ["(A)  3", "(B)  2", "(C)  2.5", "(D)  1"]
    },
    {
        "q": "34. Three wires A, B and C of same material and cross-section but lengths L, 2L and 3L are connected in parallel (same elongation). The ratio of forces F\u2090 : F\u1d47 : F\u1d9c is:",
        "opts": ["(A)  6 : 3 : 2", "(B)  1 : 2 : 3", "(C)  3 : 2 : 1", "(D)  2 : 3 : 6"]
    },
    {
        "q": "35. Two wires of same material and cross-section in series have lengths L and 2L. For the same applied force, ratio of elastic energy in wire 1 to wire 2 is:",
        "opts": ["(A)  1 : 2", "(B)  2 : 1", "(C)  1 : 4", "(D)  1 : 1"]
    },
    {
        "q": "36. Which statement about the stress-strain graph of a ductile material is WRONG?",
        "opts": ["(A)  The region beyond yield point is elastic", "(B)  Fracture point lies beyond ultimate tensile strength on the x-axis", "(C)  Hooke\u2019s law is valid up to the proportionality limit", "(D)  Yield point marks onset of plastic deformation"]
    },
    {
        "q": "37. The thermal stress in a wire (Y, linear expansion coefficient \u03b1) fixed at both ends when temperature rises by \u0394T is:",
        "opts": ["(A)  Y\u03b1\u0394T", "(B)  \u03b1\u0394T / Y", "(C)  Y / (\u03b1\u0394T)", "(D)  \u03b1 / (Y\u0394T)"]
    },
    {
        "q": "38. A wire is stretched by 1 mm when load W is applied. Work done in stretching the wire is:",
        "opts": ["(A)  W \u00d7 10\u207b\u00b3 / 2  joule", "(B)  W \u00d7 10\u207b\u00b3  joule", "(C)  2W \u00d7 10\u207b\u00b3  joule", "(D)  W\u00b2 \u00d7 10\u207b\u00b3  joule"]
    },
    {
        "q": "39. Which of the following correctly relates Y, K and G for an isotropic material?",
        "opts": ["(A)  Y = 9KG / (3K + G)", "(B)  Y = 3K + 2G", "(C)  1/Y = 1/(3K) + 1/G", "(D)  Y = KG / (K + G)"]
    },
    {
        "q": "40. A wire of natural length L\u2080 and area A\u2080 is compressed by \u0394L. With Poisson\u2019s ratio \u03c3, the new cross-sectional area is approximately:",
        "opts": ["(A)  A\u2080[1 + 2\u03c3\u0394L/L\u2080]", "(B)  A\u2080[1 \u2212 2\u03c3\u0394L/L\u2080]", "(C)  A\u2080[1 + \u03c3\u0394L/L\u2080]", "(D)  A\u2080[1 \u2212 \u03c3\u0394L/L\u2080]"]
    },
    {
        "q": "41. If stress \u221d (strain)\u207f for a material, the elastic energy density is:",
        "opts": ["(A)  stress \u00d7 strain / (n + 1)", "(B)  stress \u00d7 strain / 2", "(C)  stress / (n \u00d7 strain)", "(D)  stress \u00d7 strain \u00d7 n"]
    },
    {
        "q": "42. A ball is subjected to uniform pressure P. The fractional change in its radius \u0394R/R in terms of Y and Poisson\u2019s ratio \u03c3 is:",
        "opts": ["(A)  \u2212P(1 \u2212 2\u03c3) / Y", "(B)  \u22123P(1 \u2212 2\u03c3) / Y", "(C)  \u2212P / Y", "(D)  \u2212P(1 + \u03c3) / Y"]
    },
    {
        "q": "43. When a torque is applied to one end of a wire clamped at the other, the elastic constant being tested is:",
        "opts": ["(A)  Modulus of rigidity", "(B)  Young\u2019s modulus", "(C)  Bulk modulus", "(D)  Compressibility"]
    },
    {
        "q": "44. Among steel, copper, rubber and glass, which has the highest Young\u2019s modulus?",
        "opts": ["(A)  Steel", "(B)  Copper", "(C)  Rubber", "(D)  Glass"]
    },
    {
        "q": "45. In the elastic region, the ratio of stress to strain for a wire:",
        "opts": ["(A)  Is constant and equals the Young\u2019s modulus", "(B)  Increases with stress", "(C)  Decreases with strain", "(D)  Equals half the modulus of rigidity"]
    },
    {
        "q": "46. When a wire is stretched within the elastic limit, which energy transformation is correct?",
        "opts": ["(A)  Work done on wire is stored as elastic potential energy", "(B)  Work done is lost as heat", "(C)  Kinetic energy converts to elastic energy", "(D)  Gravitational PE converts to elastic PE"]
    },
    {
        "q": "47. A copper wire (Y = 1.2\u00d710\u00b9\u00b9 Pa, \u03c3 = 0.33, area = 1.2\u00d710\u207b\u00b3 m\u00b2, length = 4 m) is stretched by F = 4.8\u00d710\u2074 N. The lateral strain is approximately:",
        "opts": ["(A)  1.1\u00d710\u207b\u2074", "(B)  3.3\u00d710\u207b\u2074", "(C)  4.4\u00d710\u207b\u2074", "(D)  2.2\u00d710\u207b\u2074"]
    },
    {
        "q": "48. The proportionality limit, elastic limit and yield point on a stress-strain graph appear in which order from the origin?",
        "opts": ["(A)  Proportionality limit \u2192 elastic limit \u2192 yield point", "(B)  Yield point \u2192 elastic limit \u2192 proportionality limit", "(C)  Elastic limit \u2192 proportionality limit \u2192 yield point", "(D)  All three coincide for all materials"]
    },
    {
        "q": "49. A wire of length L and area A has spring constant k = YA/L. If it is cut into three equal pieces and connected in parallel, the effective spring constant is:",
        "opts": ["(A)  9k", "(B)  3k", "(C)  k/3", "(D)  k/9"]
    },
    {
        "q": "50. Steel is preferred over copper for suspension bridges because:",
        "opts": ["(A)  Steel has greater Young\u2019s modulus and greater elastic limit", "(B)  Steel is cheaper than copper", "(C)  Steel has lower density", "(D)  Steel has lower Young\u2019s modulus making it more flexible"]
    },
]

doc = SimpleDocTemplate(
    OUTPUT, pagesize=A4,
    leftMargin=2.0*cm, rightMargin=2.0*cm,
    topMargin=2.2*cm, bottomMargin=2.2*cm,
    title="Mechanical Properties of Solids \u2013 50 MCQs (NEET Hard)",
    author="Orris AI"
)

title_s = ParagraphStyle("T", fontSize=18, fontName="Helvetica-Bold",
    textColor=colors.HexColor("#0d1b5e"), alignment=TA_CENTER, spaceAfter=3)
sub_s   = ParagraphStyle("S", fontSize=10, fontName="Helvetica",
    textColor=colors.HexColor("#455a64"), alignment=TA_CENTER, spaceAfter=2)
tag_s   = ParagraphStyle("G", fontSize=9.5, fontName="Helvetica-Bold",
    textColor=colors.HexColor("#c62828"), alignment=TA_CENTER, spaceAfter=16)
q_s     = ParagraphStyle("Q", fontSize=10.5, fontName="Helvetica-Bold",
    leading=15, textColor=colors.HexColor("#0d0d0d"), spaceAfter=5, spaceBefore=10)
opt_s   = ParagraphStyle("O", fontSize=10, fontName="Helvetica",
    leading=14, leftIndent=18, textColor=colors.HexColor("#212121"), spaceAfter=2)
instr_s = ParagraphStyle("IP", fontSize=9.5, fontName="Helvetica", leading=13,
    textColor=colors.HexColor("#212121"))

story = []

story.append(Spacer(1, 0.2*cm))
story.append(Paragraph("Mechanical Properties of Solids", title_s))
story.append(Paragraph("50 Multiple Choice Questions  \u2022  NEET Level  \u2022  Hard", sub_s))
story.append(Paragraph("Physics \u2013 Class XI  \u2022  200 Marks  \u2022  Suggested Time: 60 Minutes", tag_s))
story.append(HRFlowable(width="100%", thickness=1.5, color=colors.HexColor("#0d1b5e")))
story.append(Spacer(1, 0.4*cm))

instr_box = Table(
    [[Paragraph(
        "<b>Instructions:</b>  Each question carries 4 marks. "
        "There is a negative marking of <b>\u20131</b> for each wrong answer. "
        "Choose the single best option.",
        instr_s
    )]],
    colWidths=[16.6*cm]
)
instr_box.setStyle(TableStyle([
    ("BOX",           (0,0),(-1,-1), 0.8, colors.HexColor("#7986cb")),
    ("BACKGROUND",    (0,0),(-1,-1), colors.HexColor("#f0f4ff")),
    ("TOPPADDING",    (0,0),(-1,-1), 7),
    ("BOTTOMPADDING", (0,0),(-1,-1), 7),
    ("LEFTPADDING",   (0,0),(-1,-1), 10),
    ("RIGHTPADDING",  (0,0),(-1,-1), 10),
]))
story.append(instr_box)
story.append(Spacer(1, 0.5*cm))

for i, item in enumerate(questions, start=1):
    if i > 1 and (i - 1) % 10 == 0:
        story.append(Spacer(1, 0.1*cm))
        story.append(HRFlowable(width="100%", thickness=0.5,
                                color=colors.HexColor("#b0bec5"), dash=(4, 3)))
        story.append(Spacer(1, 0.1*cm))

    block = [Paragraph(item["q"], q_s)]
    for opt in item["opts"]:
        block.append(Paragraph(opt, opt_s))
    block.append(Spacer(1, 0.1*cm))
    story.append(KeepTogether(block))

doc.build(story)
print("Done:", OUTPUT)