NEET Mechanical Properties of Solids — Set 14

Question 1

A brass block of dimensions $ 0.5 \, \text{m} \times 0.2 \, \text{m} \times 0.1 \, \text{m} $ is subjected to a shearing force of $ 5 \times 10^4 \, \text{N} $. If the shear modulus of brass is $ 3.6 \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 = 0.5 \times 0.2 = 0.1 \, \text{m}^2 $. Shear stress: $ \frac{5 \times 10^4}{0.1} = 5 \times 10^5 \, \text{N/m}^2 $. Shear strain: $ \text{Shear strain} = \frac{\text{Shear stress}}{G} = \frac{5 \times 10^5}{3.6 \times 10^{10}} \approx 1.39 \times 10^{-5} $.

Question 2

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

Accepted Answer

Understanding elastic properties ensures that materials can withstand various loads (traffic, wind, weight) without undergoing permanent deformation, maintaining structural integrity.

Question 3

A copper wire of length $ 2.8 \, \text{m} $ and cross-sectional area $ 2 \times 10^{-6} \, \text{m}^2 $ is stretched by a force of $ 160 \, \text{N} $. If the Young's modulus of copper is $ 1.1 \times 10^{11} \, \text{N/m}^2 $, what is the elongation?

Accepted Answer

Young's modulus: $ Y = \frac{F L}{A \Delta L} $. Rearrange: $ \Delta L = \frac{F L}{A Y} $. Substitute: $ \Delta L = \frac{160 \times 2.8}{2 \times 10^{-6} \times 1.1 \times 10^{11}} = \frac{448}{2.2 \times 10^5} \approx 2.04 \times 10^{-3} \, \text{m} = 2.04 \, \text{mm} $.

NEET Physics: Mechanical Properties of Solids — Practice Set 14

Q1. A brass block of dimensions \( 0.5 \, \text{m} \times 0.2 \, \text{m} \times 0.1 \, \text{m} \) is subjected to a shearing force of \( 5 \times 10^4 \, \text{N} \). If the shear modulus of brass is \( 3.6 \times 10^{10} \, \text{N/m}^2 \), what is the shear strain?

Q2. In designing bridges, why is it critical to understand the elastic properties of materials?

Q3. A copper wire of length \( 2.8 \, \text{m} \) and cross-sectional area \( 2 \times 10^{-6} \, \text{m}^2 \) is stretched by a force of \( 160 \, \text{N} \). If the Young's modulus of copper is \( 1.1 \times 10^{11} \, \text{N/m}^2 \), what is the elongation?

Q4. A steel rod of length 1 m and diameter 2 mm is subjected to a tensile force producing a stress of 5 × 10 7 N/m 2 . What is the force applied? (Take π ≈ 3.14)

Q5. Which of the following best defines stress in the context of mechanical properties of solids?

Q6. A steel wire of length \( 2.6 \, \text{m} \) and cross-sectional area \( 2 \times 10^{-6} \, \text{m}^2 \) is stretched by \( 0.52 \, \text{mm} \). If the Young's modulus of steel is \( 2 \times 10^{11} \, \text{N/m}^2 \), what is the force applied?

Q7. What does the steepness of the initial linear portion of a stress-strain curve indicate?

Q8. A steel wire of length \( 2.0 \, \text{m} \) and cross-sectional area \( 2.5 \times 10^{-6} \, \text{m}^2 \) is stretched by a force of \( 250 \, \text{N} \). If the Young's modulus of steel is \( 2 \times 10^{11} \, \text{N/m}^2 \), what is the strain produced?

Q9. A steel wire and a copper wire have the same length and cross-sectional area. Both are stretched by the same force. If Young's modulus of steel is 2 × 10 11 N/m 2 and that of copper is 1.1 × 10 11 N/m 2 , what is the ratio of elongation of the steel wire to the copper wire?

Q10. What characterizes the stress-strain behavior of a material in the region where plastic deformation begins?