NEET Mechanical Properties of Solids — Set 4

Question 1

Which modulus describes a material’s resistance to volume change under uniform pressure in all directions?

Accepted Answer

The bulk modulus measures a material’s resistance to volume change when subjected to uniform pressure (hydraulic stress) in all directions, affecting volume but not shape.

Question 2

A steel wire of length $ 2.2 \, \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?

Accepted Answer

Stress: $ \text{Stress} = \frac{F}{A} = \frac{250}{2.5 \times 10^{-6}} = 1 \times 10^8 \, \text{N/m}^2 $. Young's modulus: $ Y = \frac{\text{Stress}}{\text{Strain}} $. Strain: $ \text{Strain} = \frac{\text{Stress}}{Y} = \frac{1 \times 10^8}{2 \times 10^{11}} = 5 \times 10^{-4} $.

Question 3

An aluminium rod of length $ 1.2 \, \text{m} $ and cross-sectional area $ 2.5 \times 10^{-6} \, \text{m}^2 $ is compressed by a force producing a strain of $ 2 \times 10^{-4} $. If the Young's modulus of aluminium is $ 7 \times 10^{10} \, \text{N/m}^2 $, what is the stress?

Accepted Answer

Young's modulus: $ Y = \frac{\text{Stress}}{\text{Strain}} $. Stress: $ \text{Stress} = Y \times \text{Strain} = 7 \times 10^{10} \times 2 \times 10^{-4} = 1.4 \times 10^7 \, \text{N/m}^2 $.

NEET Physics: Mechanical Properties of Solids — Practice Set 4

Q1. Which modulus describes a material’s resistance to volume change under uniform pressure in all directions?

Q2. A steel wire of length \( 2.2 \, \text{m} \) 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?

Q3. An aluminium rod of length \( 1.2 \, \text{m} \) and cross-sectional area \( 2.5 \times 10^{-6} \, \text{m}^2 \) is compressed by a force producing a strain of \( 2 \times 10^{-4} \). If the Young's modulus of aluminium is \( 7 \times 10^{10} \, \text{N/m}^2 \), what is the stress?

Q4. A brass block of dimensions 0.3 m × 0.2 m × 0.1 m is subjected to a shearing force of 5 × 10 4 N. If the shear modulus of brass is 3.6 × 10 10 N/m 2 , what is the displacement of the upper face?

Q5. A steel wire of length \( 2.4 \, \text{m} \) and cross-sectional area \( 4 \times 10^{-6} \, \text{m}^2 \) is stretched by \( 0.6 \, \text{mm} \). If the Young's modulus of steel is \( 2 \times 10^{11} \, \text{N/m}^2 \), what is the stress?

Q6. A copper block of dimensions 0.5 m × 0.3 m × 0.2 m is subjected to a shearing force of 7 × 10 4 N on its top face. If the shear modulus of copper is 4.2 × 10 10 N/m 2 , what is the shear strain?

Q7. What does the term "elastic limit" refer to in the context of a material’s stress-strain behavior?

Q8. An aluminium block of dimensions \( 0.5 \, \text{m} \times 0.3 \, \text{m} \times 0.1 \, \text{m} \) is subjected to a shearing force of \( 7 \times 10^4 \, \text{N} \). If the shear modulus of aluminium is \( 2.5 \times 10^{10} \, \text{N/m}^2 \), what is the displacement of the top face?

Q9. A brass wire of length \( 2.6 \, \text{m} \) and cross-sectional area \( 4 \times 10^{-6} \, \text{m}^2 \) is stretched by a force of \( 400 \, \text{N} \). If the Young's modulus of brass is \( 9 \times 10^{10} \, \text{N/m}^2 \), what is the elongation?

Q10. A steel rod of length 0.5 m and cross-sectional area 1 × 10 -5 m 2 is compressed by a force of 500 N. If the strain is 5 × 10 -4 , what is the Young's modulus?