Questions covering concepts like stress, strain, Young's modulus, Hooke's law, and elastic energy in solids. Tests understanding of material behavior under load and practical applications in engineering and physics.
Strain: Strain = ΔLL. Rearrange: ΔL = Strain×L = 1.5×10−4×2.8 = 4.2×10−4m = 0.42mm. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 0.42mm. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: University Physics, Chapter 17: Thermal Expansion.
Bulk modulus: B = −pΔVV. Rearrange: ΔVV = −pB = −5×1063.7×1010≈−1.35×10−4. Magnitude: 1.35×10−4. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1.35×10−4. This satisfies dimensional consistency and physical conditions given, so option A is scientifically correct.
Ref: NCBI Bookshelf, Ideal Gas Law: P1V1/T1 = P2V2/T2.
Young's modulus: Y = FLAΔL. Rearrange: F = YAΔLL. Substitute: ΔL = 0.4×10−3m. F = 2×1011×3×10−6×0.4×10−32 = 2402 = 120N. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 120N. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.
Ref: University Physics, Chapter 17: Thermal Expansion.
Stress: Stress = F / A = 1000 / (1 × 10-5) = 1 × 108 N/m2. Young's modulus: Y = Stress / Strain. Strain: Strain = Stress / Y = (1 × 108) / (2 × 1011) = 5 × 10-4.
Ref: University Physics, Chapter 17: Thermal Expansion.
Bulk modulus: B = −pΔVV. Rearrange: ΔVV = −pB = −5×1063.7×1010≈−1.35×10−4. Change in volume: ΔV = ΔVV×V = −1.35×10−4×0.03≈−4.05×10−6m3. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 4.05×10−6m3. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCBI Bookshelf, Ideal Gas Law: P1V1/T1 = P2V2/T2.
Stress: Stress = F / A = 1000 / (5 × 10-6) = 2 × 108 N/m2. Young's modulus: Y = Stress / Strain. Strain: Strain = Stress / Y = (2 × 108) / (9 × 1010) ≈ 2.22 × 10-3.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
A ductile material undergoes significant plastic deformation before fracture, allowing it to withstand larger strains, while a brittle material fractures with minimal plastic deformation. As per NCERT, applying relevant law/formula with correct units and sign convention leads to Ductile materials undergo significant plastic deformation before fracture. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
Strain: Strain = ΔLL = 0.7×10−32.8 = 2.5×10−4. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.5×10−4. This satisfies dimensional consistency and physical conditions given, so option D is scientifically correct.
Ref: University Physics, Chapter 17: Thermal Expansion.
Shear modulus: G = (Shear stress) / (Shear strain). Shear stress: Shear stress = F / A = (4 × 104) / 0.05 = 8 × 105 N/m2. Shear strain: 2 × 10-5. Substitute: G = (8 × 105) / (2 × 10-5) = 4 × 1010 N/m2.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
Young's modulus: Y = StressStrain. Stress: Stress = Y×Strain = 9×1010×4×10−4 = 3.6×107N/m2. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 3.6×107N/m2. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
Shear modulus: G = Shear stressShear strain. Shear stress: Shear stress = FA, A = 0.5×0.3 = 0.15m2. Shear stress: 5×1040.15≈3.33×105N/m2. Shear strain: Shear strain = Shear stressG = 3.33×1058.4×1010≈3.96×10−6.
Ref: University Physics, Chapter 17: Thermal Expansion.
Young's modulus: Y = StressStrain. Stress: Stress = Y×Strain = 9×1010×2×10−4 = 1.8×107N/m2. Force: F = Stress×A = 1.8×107×2×10−6 = 36N. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 36N. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
