Question 1

A steel wire of length 2 m and cross-sectional area 1 mm² is stretched by a force of 100 N. If Young's modulus of steel is 2 × 10¹¹ Pa, what is the extension produced in the wire?

Accepted Answer

Using Y = (F/A)/(ΔL/L), extension ΔL = (F × L)/(A × Y) = (100 × 2)/(10⁻⁶ × 2 × 10¹¹) = 1 mm.

Question 2

The stress-strain curve of a material shows a linear relationship up to point P, after which it becomes non-linear. What does point P represent?

Accepted Answer

Point P where the stress-strain curve deviates from linearity represents the elastic limit, beyond which permanent deformation occurs.

Question 3

A copper rod experiences a tensile stress of 5 × 10⁷ Pa. If Young's modulus of copper is 1.3 × 10¹¹ Pa, what is the tensile strain produced?

Accepted Answer

Strain = Stress / Young's modulus = (5 × 10⁷) / (1.3 × 10¹¹) ≈ 3.8 × 10⁻⁴.

Question 4

When a rubber ball is squeezed and then released, it returns to its original shape. Which property of the material is responsible for this behavior?

Accepted Answer

Elasticity is the property of a material to return to its original shape after the deforming force is removed.

Question 5

A wire of diameter 2 mm is subjected to a tensile force of 200 N. What is the tensile stress in the wire? (Take π ≈ 3.14)

Accepted Answer

Stress = Force / Area = 200 / (π × (10⁻³)²) = 200 / (3.14 × 10⁻⁶) ≈ 6.37 × 10⁷ Pa.

Question 6

A steel wire of length 2 m and cross-sectional area 1 mm² is stretched by a force of 100 N. If Young's modulus of steel is 2 × 10¹¹ Pa, calculate the extension produced in the wire.

Accepted Answer

Using Young's modulus Y = (F/A) × (L/ΔL), we get ΔL = (F × L)/(Y × A) = (100 × 2)/(2×10¹¹ × 10⁻⁶) = 1 mm.

Question 7

Define the term 'elastic limit' in the context of mechanical properties of solids.

Accepted Answer

Elastic limit is the maximum stress up to which a material returns to its original dimensions after the deforming force is removed.

Question 8

A copper wire experiences a tensile stress of 5 × 10⁷ Pa, producing a strain of 0.0025. Calculate Young's modulus for copper.

Accepted Answer

Young's modulus Y = stress/strain = (5 × 10⁷)/(0.0025) = 2 × 10¹⁰ Pa.

Question 9

Which of the following statements correctly defines 'Poisson's ratio'?

Accepted Answer

Poisson's ratio (σ) = lateral strain/longitudinal strain; it measures how much a material contracts perpendicular to the direction of loading.

Question 10

A rubber ball is compressed uniformly from all sides by an external pressure of 2 × 10⁶ Pa, and its volume decreases by 2%. Calculate the bulk modulus of the rubber.

Accepted Answer

Bulk modulus K = pressure/(volumetric strain) = (2 × 10⁶)/(0.02) = 1 × 10⁸ Pa.

Question 11

A metal rod of length 1 m is subjected to a shear force such that the top surface is displaced by 0.5 mm relative to the bottom. If the shear modulus is 8 × 10¹⁰ Pa, find the shear stress developed.

Accepted Answer

Shear modulus G = shear stress/shear strain; shear strain = displacement/length = 0.5×10⁻³/1 = 5×10⁻⁴, so shear stress = 8×10¹⁰ × 5×10⁻⁴ = 4×10⁸ Pa.

Question 12

Which mechanical property describes the ability of a material to resist permanent deformation under stress?

Accepted Answer

Elasticity is the property of materials to return to their original shape and size after the deforming force is removed.

Question 13

A cylindrical steel rod has a cross-sectional area of 2 cm² and length 50 cm. If it is stretched by 0.5 mm under a load, and Young's modulus is 2 × 10¹¹ Pa, find the magnitude of the applied force.

Accepted Answer

From Y = (F/A) × (L/ΔL), F = (Y × A × ΔL)/L = (2×10¹¹ × 2×10⁻⁴ × 0.5×10⁻³)/0.5 = 4×10⁴ N.

Question 14

The stress-strain curve of a material shows a linear region followed by a curved region and finally fracture. The linear region represents which property?

Accepted Answer

The linear portion of the stress-strain curve (below the elastic limit) represents elastic deformation where stress is proportional to strain.

Question 15

A steel wire of length 2 m and cross-sectional area 1 mm² is stretched by a force of 100 N. If Young's modulus for steel is 2 × 10¹¹ Pa, calculate the extension produced in the wire.

Accepted Answer

Using Young's modulus formula Y = (F/A)/(ΔL/L), we get ΔL = (F × L)/(Y × A) = (100 × 2)/(2 × 10¹¹ × 10⁻⁶) = 1 mm.

Question 16

When a wire is subjected to tensile stress, its Poisson's ratio is defined as the ratio of lateral strain to longitudinal strain. If a copper wire experiences a longitudinal strain of 0.002 and Poisson's ratio is 0.34, what is the lateral strain?

Accepted Answer

Poisson's ratio μ = lateral strain / longitudinal strain; lateral strain = μ × longitudinal strain = 0.34 × 0.002 = 0.00068 = 6.8 × 10⁻⁴.

Question 17

A material exhibits elastic behavior up to a stress of 400 MPa, beyond which plastic deformation begins. If the Young's modulus is 200 GPa, what is the elastic limit strain of this material?

Accepted Answer

Elastic limit strain = stress / Young's modulus = (400 × 10⁶ Pa) / (200 × 10⁹ Pa) = 0.002 = 2 × 10⁻³.

Question 18

Two wires A and B made of the same material have lengths in ratio 1:2 and diameters in ratio 2:1. If both wires experience the same tensile stress, the ratio of their extensions will be:

Accepted Answer

Extension ΔL = (stress × L) / Y; with L_A:L_B = 1:2 and A_A:A_B = 4:1 (diameter ratio 2:1), extension ratio ΔL_A:ΔL_B = (1/4):(2/1) = 1:8.

Agniveer (All) Mechanical Properties of Solids

Mechanical Properties of Solids — Practice Questions