NEET Mechanical Properties of Solids — Set 1

Question 1

A copper block of dimensions $ 0.4 \, \text{m} \times 0.2 \, \text{m} \times 0.05 \, \text{m} $ is subjected to a shearing force of $ 1.5 \times 10^4 \, \text{N} $. If the shear modulus of copper is $ 4.2 \times 10^{10} \, \text{N/m}^2 $, what is the shear strain?

Accepted Answer

Shear modulus: $ G = \frac{\text{Shear stress}}{\text{Shear strain}} $. Shear stress: $ \text{Shear stress} = \frac{F}{A} $, $ A = 0.4 \times 0.2 = 0.08 \, \text{m}^2 $. Shear stress: $ \frac{1.5 \times 10^4}{0.08} = 1.875 \times 10^5 \, \text{N/m}^2 $. Shear strain: $ \text{Shear strain} = \frac{\text{Shear stress}}{G} = \frac{1.875 \times 10^5}{4.2 \times 10^{10}} \approx 4.46 \times 10^{-6} $.

Question 2

A steel wire of length 3 m and cross-sectional area 4 × 10 -6 m 2 is stretched by 0.3 mm. If the Young's modulus of steel is 2 × 10 11 N/m 2 , what is the force applied?

Accepted Answer

Young's modulus: Y = (F L) / (A ΔL). Rearrange: F = (Y A ΔL) / L. Substitute: ΔL = 0.3 × 10 -3 m, so F = (2 × 10 11 × 4 × 10 -6 × 0.3 × 10 -3 ) / 3 = 80 N.

Question 3

A steel wire of length 4 m and cross-sectional area 2 × 10 -6 m 2 is stretched by 0.4 mm. If the force applied is 200 N, what is the Young's modulus of the steel?

Accepted Answer

Young's modulus: Y = (F L) / (A ΔL). Substitute: ΔL = 0.4 × 10 -3 m. Y = (200 × 4) / (2 × 10 -6 × 0.4 × 10 -3 ) = 800 / (8 × 10 -10 ) = 1 × 10 12 N/m 2 .

NEET Physics: Mechanical Properties of Solids — Practice Set 1

Q1. A copper block of dimensions \( 0.4 \, \text{m} \times 0.2 \, \text{m} \times 0.05 \, \text{m} \) is subjected to a shearing force of \( 1.5 \times 10^4 \, \text{N} \). If the shear modulus of copper is \( 4.2 \times 10^{10} \, \text{N/m}^2 \), what is the shear strain?

Q2. A steel wire of length 3 m and cross-sectional area 4 × 10 -6 m 2 is stretched by 0.3 mm. If the Young's modulus of steel is 2 × 10 11 N/m 2 , what is the force applied?

Q3. A steel wire of length 4 m and cross-sectional area 2 × 10 -6 m 2 is stretched by 0.4 mm. If the force applied is 200 N, what is the Young's modulus of the steel?

Q4. An aluminium rod of length \( 1.6 \, \text{m} \) and cross-sectional area \( 2 \times 10^{-6} \, \text{m}^2 \) is compressed by a force of \( 600 \, \text{N} \). If the Young's modulus of aluminium is \( 7 \times 10^{10} \, \text{N/m}^2 \), what is the compression?

Q5. Why is steel often chosen over materials like copper for heavy-duty structural applications?

Q6. What does the steepness of the linear portion of a stress-strain curve typically indicate about a material?

Q7. A water sample of volume 1 litre is compressed by 0.05%. If the bulk modulus of water is 2.2 × 10 9 N/m 2 , what is the pressure applied?

Q8. Which type of stress leads to a change in length of a body without changing its shape?

Q9. What does the term "elastic limit" refer to in the context of a material’s stress-strain behavior?

Q10. Which of the following best defines stress in the context of mechanical properties of solids?