NEET Mechanical Properties of Solids — Set 11

Question 1

A glass slab of volume $ 0.04 \, \text{m}^3 $ is subjected to a hydraulic pressure of $ 7 \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 fractional change in volume?

Accepted Answer

Bulk modulus: $ B = -\frac{p}{\frac{\Delta V}{V}} $. Rearrange: $ \frac{\Delta V}{V} = -\frac{p}{B} = -\frac{7 \times 10^6}{3.7 \times 10^{10}} \approx -1.89 \times 10^{-4} $. Magnitude: $ 1.89 \times 10^{-4} $.

Question 2

A copper wire of length $ 2.0 \, \text{m} $ and cross-sectional area $ 2 \times 10^{-6} \, \text{m}^2 $ is stretched by a force producing a strain of $ 1 \times 10^{-4} $. If the Young's modulus of copper is $ 1.1 \times 10^{11} \, \text{N/m}^2 $, what is the force applied?

Accepted Answer

Young's modulus: $ Y = \frac{\text{Stress}}{\text{Strain}} $. Stress: $ \text{Stress} = Y \times \text{Strain} = 1.1 \times 10^{11} \times 1 \times 10^{-4} = 1.1 \times 10^7 \, \text{N/m}^2 $. Force: $ F = \text{Stress} \times A = 1.1 \times 10^7 \times 2 \times 10^{-6} = 22 \, \text{N} $.

Question 3

An aluminium wire of length $ 1.5 \, \text{m} $ and cross-sectional area $ 2 \times 10^{-6} \, \text{m}^2 $ is stretched by a force of $ 140 \, \text{N} $. If the Young's modulus of aluminium is $ 7 \times 10^{10} \, \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{140 \times 1.5}{2 \times 10^{-6} \times 7 \times 10^{10}} = \frac{210}{1.4 \times 10^5} = 1.5 \times 10^{-3} \, \text{m} = 1.5 \, \text{mm} $.

NEET Physics: Mechanical Properties of Solids — Practice Set 11

Q1. A glass slab of volume \( 0.04 \, \text{m}^3 \) is subjected to a hydraulic pressure of \( 7 \times 10^6 \, \text{N/m}^2 \). If the bulk modulus of glass is \( 3.7 \times 10^{10} \, \text{N/m}^2 \), what is the fractional change in volume?

Q2. A copper wire of length \( 2.0 \, \text{m} \) and cross-sectional area \( 2 \times 10^{-6} \, \text{m}^2 \) is stretched by a force producing a strain of \( 1 \times 10^{-4} \). If the Young's modulus of copper is \( 1.1 \times 10^{11} \, \text{N/m}^2 \), what is the force applied?

Q3. An aluminium wire of length \( 1.5 \, \text{m} \) and cross-sectional area \( 2 \times 10^{-6} \, \text{m}^2 \) is stretched by a force of \( 140 \, \text{N} \). If the Young's modulus of aluminium is \( 7 \times 10^{10} \, \text{N/m}^2 \), what is the elongation?

Q4. An aluminium wire of length \( 1.7 \, \text{m} \) and cross-sectional area \( 2 \times 10^{-6} \, \text{m}^2 \) is stretched by \( 0.34 \, \text{mm} \). If the Young's modulus of aluminium is \( 7 \times 10^{10} \, \text{N/m}^2 \), what is the force applied?

Q5. In the stress-strain behavior of a ductile material, what happens after the maximum stress the material can endure?

Q6. Which modulus is not applicable for describing the elastic behavior of liquids and gases under shear stress?

Q7. A brass wire of length \( 2.0 \, \text{m} \) and cross-sectional area \( 3 \times 10^{-6} \, \text{m}^2 \) is stretched by a force producing a strain of \( 5 \times 10^{-4} \). If the Young's modulus of brass is \( 9 \times 10^{10} \, \text{N/m}^2 \), what is the force applied?

Q8. A steel rod of length 0.6 m and cross-sectional area 5 × 10 -6 m 2 is compressed by a force producing a strain of 3 × 10 -4 . If the Young's modulus of steel is 2 × 10 11 N/m 2 , what is the force applied?

Q9. What characterizes the stress-strain behavior of a material in the region where plastic deformation begins?

Q10. A copper wire of length 1.2 m and cross-sectional area 1.5 × 10 -6 m 2 is stretched by a force producing a stress of 2 × 10 7 N/m 2 . If the Young's modulus of copper is 1.1 × 10 11 N/m 2 , what is the strain?