NEET Mechanical Properties of Solids — Set 9

Question 1

A cylindrical rod of length 0.5 m and radius 0.01 m is compressed by a force of 5000 N. If the compressive stress is 5 × 10 6 N/m 2 , what is the cross-sectional area of the rod?

Accepted Answer

Stress: Stress = F / A. Rearrange: A = F / Stress. Substitute: A = 5000 / (5 × 10 6 ) = 10 -3 m 2 .

Question 2

A steel wire of length $ 2.5 \, \text{m} $ and cross-sectional area $ 3.5 \times 10^{-6} \, \text{m}^2 $ is stretched by a force of $ 350 \, \text{N} $. If the elongation is $ 0.2 \, \text{mm} $, what is the Young's modulus of steel?

Accepted Answer

Young's modulus: $ Y = \frac{F L}{A \Delta L} $. Substitute: $ \Delta L = 0.2 \times 10^{-3} \, \text{m} $. $ Y = \frac{350 \times 2.5}{3.5 \times 10^{-6} \times 0.2 \times 10^{-3}} = \frac{875}{7 \times 10^{-10}} \approx 1.25 \times 10^{12} \, \text{N/m}^2 $.

Question 3

Why do engineers prefer materials with a large Young’s modulus for designing columns and beams?

Accepted Answer

Materials with a large Young’s modulus are stiffer, requiring greater force to produce small deformations, which ensures better resistance to bending and stretching.

NEET Physics: Mechanical Properties of Solids — Practice Set 9

Q1. A cylindrical rod of length 0.5 m and radius 0.01 m is compressed by a force of 5000 N. If the compressive stress is 5 × 10 6 N/m 2 , what is the cross-sectional area of the rod?

Q2. A steel wire of length \( 2.5 \, \text{m} \) and cross-sectional area \( 3.5 \times 10^{-6} \, \text{m}^2 \) is stretched by a force of \( 350 \, \text{N} \). If the elongation is \( 0.2 \, \text{mm} \), what is the Young's modulus of steel?

Q3. Why do engineers prefer materials with a large Young’s modulus for designing columns and beams?

Q4. Why are I-shaped beams commonly used in construction for load-bearing applications?

Q5. An aluminium wire of length \( 2.5 \, \text{m} \) and cross-sectional area \( 1.5 \times 10^{-6} \, \text{m}^2 \) is stretched by a force of \( 150 \, \text{N} \). If the Young's modulus of aluminium is \( 7 \times 10^{10} \, \text{N/m}^2 \), what is the stress?

Q6. An aluminium block of dimensions \( 0.3 \, \text{m} \times 0.2 \, \text{m} \times 0.05 \, \text{m} \) is subjected to a shearing force of \( 1.5 \times 10^4 \, \text{N} \). If the shear modulus of aluminium is \( 2.5 \times 10^{10} \, \text{N/m}^2 \), what is the shear strain?

Q7. Why do engineers prefer materials with a large Young’s modulus for designing columns and beams?

Q8. A steel rod of length 0.8 m and cross-sectional area 2 × 10 -5 m 2 is compressed by a force of 800 N. If the Young's modulus of steel is 2 × 10 11 N/m 2 , what is the compression?

Q9. In designing bridges, why is it critical to understand the elastic properties of materials?

Q10. A glass slab of volume 0.005 m 3 is compressed by a pressure of 3 × 10 6 N/m 2 . If the bulk modulus of glass is 3.7 × 10 10 N/m 2 , what is the change in volume?