11 public questions tagged with this topic.
Young's modulus: Y = Stress / Strain. Stress: Stress = F / A = 150 / (3 × 10-6) = 5 × 107 N/m2. Strain: 1 × 10-3. So, Y = (5 × 107) / (1 × 10-3) = 5 × 1010 N/m2.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
Stress: Stress = FA = 1501.5×10−6 = 1×108N/m2. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1×108N/m2. This satisfies dimensional consistency and physical conditions given, so option A is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
Young's modulus: Y = (F L) / (A ΔL). Rearrange: ΔL = (F L) / (A Y). Substitute: ΔL = (800 × 0.8) / (2 × 10-5 × 2 × 1011) = 640 / (4 × 106) = 1.6 × 10-4 m = 0.16 mm.
Ref: University Physics, Chapter 17: Thermal Expansion.
Shear modulus: G = Shear stressShear strain. Shear stress: Shear stress = FA, A = 0.3×0.2 = 0.06m2. Shear stress: 1.5×1040.06 = 2.5×105N/m2. Shear strain: Shear strain = Shear stressG = 2.5×1052.5×1010 = 1×10−5.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
Young's modulus: Y = StressStrain. Stress: Stress = Y×Strain = 9×1010×2×10−4 = 1.8×107N/m2. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1.8×107N/m2. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
Stress: Stress = F / A. Area: A = π r2 = 3.14 × (0.015)2 = 3.14 × 0.000225 = 7.065 × 10-4 m2. Maximum force: F = Stress × A = 2 × 108 × 7.065 × 10-4 = 1.413 × 105 N.
Ref: University Physics, Chapter 17: Thermal Expansion.
Stress: Stress = F / A. Area: A = π r2 = 3.14 × (0.02)2 = 3.14 × 0.0004 = 1.256 × 10-3 m2. Maximum force: F = Stress × A = 1 × 108 × 1.256 × 10-3 = 1.256 × 105 N.
Ref: University Physics, Chapter 17: Thermal Expansion.
Young's modulus: Y = StressStrain. Strain: Strain = StressY = 3×1077×1010≈4.29×10−4. Compression: ΔL = Strain×L = 4.29×10−4×1.4≈6×10−4m = 0.6mm. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 0.6mm. This satisfies dimensional consistency and physical conditions given, so option D is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
Shear modulus: G = Shear stressShear strain. Shear stress: Shear stress = FA, A = 0.6×0.4 = 0.24m2. Shear stress: 7×1040.24≈2.92×105N/m2. Shear strain: Shear strain = Shear stressG = 2.92×1054.2×1010≈6.95×10−6.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
Stress: Stress = FA = 4503×10−6 = 1.5×108N/m2. Young's modulus: Y = StressStrain. Strain: Strain = StressY = 1.5×1082×1011 = 7.5×10−4. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 7.5×10−4. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: University Physics, Chapter 17: Thermal Expansion.
Shear modulus: G = Shear stressShear strain. Shear stress: Shear stress = FA, A = 0.3×0.2 = 0.06m2. Shear stress: 3×1040.06 = 5×105N/m2. Shear strain: Shear strain = Shear stressG = 5×1054.2×1010≈1.19×10−5.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
