NEET Mechanical Properties of Solids — Set 8

Question 1

A brass wire of length $ 1.6 \, \text{m} $ and cross-sectional area $ 2 \times 10^{-6} \, \text{m}^2 $ is stretched by a force producing a stress of $ 4 \times 10^7 \, \text{N/m}^2 $. If the Young's modulus of brass is $ 9 \times 10^{10} \, \text{N/m}^2 $, what is the strain?

Accepted Answer

Young's modulus: $ Y = \frac{\text{Stress}}{\text{Strain}} $. Strain: $ \text{Strain} = \frac{\text{Stress}}{Y} = \frac{4 \times 10^7}{9 \times 10^{10}} \approx 4.44 \times 10^{-4} $.

Question 2

A brass wire of length $ 1.8 \, \text{m} $ and cross-sectional area $ 2.5 \times 10^{-6} \, \text{m}^2 $ is stretched by a force producing a strain of $ 2 \times 10^{-4} $. If the Young's modulus of brass is $ 9 \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} = 9 \times 10^{10} \times 2 \times 10^{-4} = 1.8 \times 10^7 \, \text{N/m}^2 $.

Question 3

A glass slab of volume $ 0.01 \, \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?

Accepted Answer

Bulk modulus: $ B = -\frac{p}{\frac{\Delta V}{V}} $. Rearrange: $ \frac{\Delta V}{V} = -\frac{p}{B} = -\frac{2 \times 10^6}{3.7 \times 10^{10}} \approx -5.41 \times 10^{-5} $. Change in volume: $ \Delta V = \frac{\Delta V}{V} \times V = -5.41 \times 10^{-5} \times 0.01 \approx -5.41 \times 10^{-7} \, \text{m}^3 $.

NEET Physics: Mechanical Properties of Solids — Practice Set 8

Q1. A brass wire of length \( 1.6 \, \text{m} \) and cross-sectional area \( 2 \times 10^{-6} \, \text{m}^2 \) is stretched by a force producing a stress of \( 4 \times 10^7 \, \text{N/m}^2 \). If the Young's modulus of brass is \( 9 \times 10^{10} \, \text{N/m}^2 \), what is the strain?

Q2. A brass wire of length \( 1.8 \, \text{m} \) and cross-sectional area \( 2.5 \times 10^{-6} \, \text{m}^2 \) is stretched by a force producing a strain of \( 2 \times 10^{-4} \). If the Young's modulus of brass is \( 9 \times 10^{10} \, \text{N/m}^2 \), what is the stress?

Q3. A glass slab of volume \( 0.01 \, \text{m}^3 \) 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?

Q4. A copper rod of length 1 m and diameter 2 mm is subjected to a tensile force. If the stress is 4 × 10 7 N/m 2 , what is the force applied? (Take π ≈ 3.14)

Q5. A steel rod of radius \( 0.01 \, \text{m} \) and length \( 1.5 \, \text{m} \) is subjected to a tensile force producing a stress of \( 4 \times 10^7 \, \text{N/m}^2 \). What is the force applied? (Take \( \pi \approx 3.14 \))

Q6. A steel wire of length \( 2.6 \, \text{m} \) and cross-sectional area \( 2 \times 10^{-6} \, \text{m}^2 \) is stretched by a force of \( 400 \, \text{N} \). If the Young's modulus of steel is \( 2 \times 10^{11} \, \text{N/m}^2 \), what is the elongation?

Q7. A brass rod of radius \( 0.008 \, \text{m} \) and length \( 1.0 \, \text{m} \) is subjected to a tensile force producing a stress of \( 5 \times 10^7 \, \text{N/m}^2 \). What is the force applied? (Take \( \pi \approx 3.14 \))

Q8. What property of a material primarily determines its resistance to uniform compression?

Q9. A brass wire of length \( 2.4 \, \text{m} \) and cross-sectional area \( 3 \times 10^{-6} \, \text{m}^2 \) is stretched by a force producing a stress of \( 5 \times 10^7 \, \text{N/m}^2 \). If the Young's modulus of brass is \( 9 \times 10^{10} \, \text{N/m}^2 \), what is the strain?

Q10. A copper block of dimensions 0.4 m × 0.3 m × 0.1 m is subjected to a shearing force of 3 × 10 4 N. If the shear modulus of copper is 4.2 × 10 10 N/m 2 , what is the displacement of the top face?