NEET Mechanical Properties of Solids — Set 10

Question 1

A copper block of dimensions $ 0.5 \, \text{m} \times 0.3 \, \text{m} \times 0.1 \, \text{m} $ is subjected to a shearing force of $ 6 \times 10^4 \, \text{N} $. If the shear modulus of copper is $ 4.2 \times 10^{10} \, \text{N/m}^2 $, what is the displacement of the top face?

Accepted Answer

Shear modulus: $ G = \frac{F / A}{\Delta x / L} $. Rearrange: $ \Delta x = \frac{F L}{A G} $. Area: $ A = 0.5 \times 0.3 = 0.15 \, \text{m}^2 $, $ L = 0.1 \, \text{m} $. Substitute: $ \Delta x = \frac{6 \times 10^4 \times 0.1}{0.15 \times 4.2 \times 10^{10}} = \frac{6000}{6.3 \times 10^9} \approx 9.52 \times 10^{-7} \, \text{m} $.

Question 2

A copper wire of length $ 2.2 \, \text{m} $ and cross-sectional area $ 1.8 \times 10^{-6} \, \text{m}^2 $ is stretched by a force of $ 180 \, \text{N} $. If the Young's modulus of copper is $ 1.1 \times 10^{11} \, \text{N/m}^2 $, what is the strain?

Accepted Answer

Stress: $ \text{Stress} = \frac{F}{A} = \frac{180}{1.8 \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}{1.1 \times 10^{11}} \approx 9.09 \times 10^{-4} $.

Question 3

A water sample of volume $ 1.5 \, \text{litres} $ is compressed by a pressure of $ 3 \times 10^6 \, \text{N/m}^2 $. If the bulk modulus of water is $ 2.2 \times 10^9 \, \text{N/m}^2 $, what is the fractional change in volume?

Accepted Answer

Bulk modulus: $ B = -\frac{p}{\frac{\Delta V}{V}} $. Rearrange: $ \frac{\Delta V}{V} = -\frac{p}{B} = -\frac{3 \times 10^6}{2.2 \times 10^9} \approx -1.36 \times 10^{-3} $. Magnitude: $ 1.36 \times 10^{-3} $.

NEET Physics: Mechanical Properties of Solids — Practice Set 10

Q1. A copper block of dimensions \( 0.5 \, \text{m} \times 0.3 \, \text{m} \times 0.1 \, \text{m} \) is subjected to a shearing force of \( 6 \times 10^4 \, \text{N} \). If the shear modulus of copper is \( 4.2 \times 10^{10} \, \text{N/m}^2 \), what is the displacement of the top face?

Q2. A copper wire of length \( 2.2 \, \text{m} \) and cross-sectional area \( 1.8 \times 10^{-6} \, \text{m}^2 \) is stretched by a force of \( 180 \, \text{N} \). If the Young's modulus of copper is \( 1.1 \times 10^{11} \, \text{N/m}^2 \), what is the strain?

Q3. A water sample of volume \( 1.5 \, \text{litres} \) is compressed by a pressure of \( 3 \times 10^6 \, \text{N/m}^2 \). If the bulk modulus of water is \( 2.2 \times 10^9 \, \text{N/m}^2 \), what is the fractional change in volume?

Q4. A steel wire of length \( 3.0 \, \text{m} \) and cross-sectional area \( 2 \times 10^{-6} \, \text{m}^2 \) is stretched by a force of \( 200 \, \text{N} \). If the Young's modulus of steel is \( 2 \times 10^{11} \, \text{N/m}^2 \), what is the elongation?

Q5. Which type of stress causes a change in the shape of a body without altering its volume?

Q6. A copper wire of length 2 m and cross-sectional area 3 × 10 -6 m 2 is stretched by a force of 150 N. If the strain produced is 1 × 10 -3 , what is the Young's modulus of copper?

Q7. A steel wire of length \( 3.2 \, \text{m} \) and cross-sectional area \( 5 \times 10^{-6} \, \text{m}^2 \) is stretched by \( 0.8 \, \text{mm} \). If the Young's modulus of steel is \( 2 \times 10^{11} \, \text{N/m}^2 \), what is the force applied?

Q8. Why is steel often chosen over materials like copper for heavy-duty structural applications?

Q9. A glass slab of volume \( 0.015 \, \text{m}^3 \) is subjected to a hydraulic pressure of \( 2 \times 10^6 \, \text{N/m}^2 \). If the bulk modulus of glass is \( 3.7 \times 10^{10} \, \text{N/m}^2 \), what is the change in volume?

Q10. A glass slab of volume \( 0.025 \, \text{m}^3 \) is subjected to a hydraulic pressure of \( 4 \times 10^6 \, \text{N/m}^2 \). If the bulk modulus of glass is \( 3.7 \times 10^{10} \, \text{N/m}^2 \), what is the change in volume?