14 public questions tagged with this topic.
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.
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 = (F L) / (A ΔL). Rearrange: ΔL = (F L) / (A Y). Substitute: ΔL = (400 × 3) / (2 × 10-6 × 9 × 1010) = 1200 / (1.8 × 105) = 6.67 × 10-3 m ≈ 6.67 mm.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
After the maximum stress (ultimate tensile strength), a ductile material experiences a decrease in stress with additional strain, leading to eventual fracture. As per NCERT, applying relevant law/formula with correct units and sign convention leads to The material begins to fracture. 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). Substitute: ΔL = 0.25 × 10-3 m. Y = (150 × 1.5) / (2.5 × 10-6 × 0.25 × 10-3) = 225 / (6.25 × 10-10) = 3.6 × 1011 N/m2.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
Young's modulus: Y = FLAΔL. Rearrange: ΔL = FLAY. Substitute: ΔL = 100×1.51×10−6×2×1011 = 1502×105 = 7.5×10−4m = 0.75mm. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 0.75mm. This satisfies dimensional consistency and physical conditions given, so option A is scientifically correct.
Ref: University Physics, Chapter 17: Thermal Expansion.
For a ductile material, after the maximum stress point (ultimate tensile strength), the stress decreases with increasing strain as the material necks, leading to fracture. As per NCERT, applying relevant law/formula with correct units and sign convention leads to The stress decreases leading to fracture. This satisfies dimensional consistency and physical conditions given, so option B 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 = (50 × 1) / (1 × 10-6 × 1.1 × 1011) = 50 / (1.1 × 105) ≈ 4.55 × 10-4 m = 0.455 mm.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
Young's modulus: Y = Stress / Strain. Stress: Stress = Y × Strain = 2 × 1011 × 2 × 10-4 = 4 × 107 N/m2. Force: F = Stress × A = 4 × 107 × 3 × 10-6 = 120 N.
Ref: University Physics, Chapter 17: Thermal Expansion.
Young's modulus: Y = StressStrain. Stress: Stress = Y×Strain = 2×1011×3×10−4 = 6×107N/m2. Force: F = Stress×A = 6×107×2×10−6 = 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.
The elastic limit is the maximum stress a material can withstand while still returning to its original shape upon removal of the load; beyond this, permanent deformation occurs. As per NCERT, applying relevant law/formula with correct units and sign convention leads to The maximum stress beyond which the material does not return to its original shape. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
