NEET Mechanical Properties of Solids — Set 5

Question 1

A copper rod of length $ 2.0 \, \text{m} $ and cross-sectional area $ 2.5 \times 10^{-6} \, \text{m}^2 $ is subjected to a tensile force of $ 500 \, \text{N} $. If the Young's modulus of copper is $ 1.1 \times 10^{11} \, \text{N/m}^2 $, what is the strain produced?

Accepted Answer

Stress: $ \text{Stress} = \frac{F}{A} = \frac{500}{2.5 \times 10^{-6}} = 2 \times 10^8 \, \text{N/m}^2 $. Young's modulus: $ Y = \frac{\text{Stress}}{\text{Strain}} $. Strain: $ \text{Strain} = \frac{\text{Stress}}{Y} = \frac{2 \times 10^8}{1.1 \times 10^{11}} \approx 1.82 \times 10^{-3} $.

Question 2

A glass slab of volume $ 0.03 \, \text{m}^3 $ is subjected to a hydraulic pressure of $ 6 \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{6 \times 10^6}{3.7 \times 10^{10}} \approx -1.62 \times 10^{-4} $. Magnitude: $ 1.62 \times 10^{-4} $.

Question 3

A solid aluminium sphere is subjected to a hydraulic pressure of 1 × 10 7 N/m 2 . If the bulk modulus of aluminium is 7.2 × 10 10 N/m 2 , what is the fractional change in volume?

Accepted Answer

Bulk modulus: B = -p / (ΔV / V). Rearrange: ΔV / V = -p / B. Substitute: ΔV / V = -(1 × 10 7 ) / (7.2 × 10 10 ) ≈ -1.39 × 10 -4 . Magnitude: 1.39 × 10 -4 .

NEET Physics: Mechanical Properties of Solids — Practice Set 5

Q1. A copper rod of length \( 2.0 \, \text{m} \) and cross-sectional area \( 2.5 \times 10^{-6} \, \text{m}^2 \) is subjected to a tensile force of \( 500 \, \text{N} \). If the Young's modulus of copper is \( 1.1 \times 10^{11} \, \text{N/m}^2 \), what is the strain produced?

Q2. A glass slab of volume \( 0.03 \, \text{m}^3 \) is subjected to a hydraulic pressure of \( 6 \times 10^6 \, \text{N/m}^2 \). If the bulk modulus of glass is \( 3.7 \times 10^{10} \, \text{N/m}^2 \), what is the fractional change in volume?

Q3. A solid aluminium sphere is subjected to a hydraulic pressure of 1 × 10 7 N/m 2 . If the bulk modulus of aluminium is 7.2 × 10 10 N/m 2 , what is the fractional change in volume?

Q4. A glass slab of volume \( 0.05 \, \text{m}^3 \) is subjected to a hydraulic pressure of \( 8 \times 10^6 \, \text{N/m}^2 \). If the bulk modulus of glass is \( 3.7 \times 10^{10} \, \text{N/m}^2 \), what is the fractional change in volume?

Q5. Why do materials like steel require a significantly larger force to produce small deformations compared to materials like rubber?

Q6. What property of a material primarily determines its resistance to uniform compression?

Q7. A copper block of dimensions \( 0.3 \, \text{m} \times 0.2 \, \text{m} \times 0.05 \, \text{m} \) is subjected to a shearing force of \( 3 \times 10^4 \, \text{N} \). If the shear modulus of copper is \( 4.2 \times 10^{10} \, \text{N/m}^2 \), what is the shear strain?

Q8. A copper wire of length 1.5 m and diameter 1 mm is subjected to a tensile force of 100 N. If the Young's modulus of copper is 1.1 × 10 11 N/m 2 , what is the stress in the wire?

Q9. What is the primary reason solids are far less compressible than gases?

Q10. An aluminium wire of length \( 2.0 \, \text{m} \) and cross-sectional area \( 1.5 \times 10^{-6} \, \text{m}^2 \) is stretched by a force of \( 150 \, \text{N} \). If the Young's modulus of aluminium is \( 7 \times 10^{10} \, \text{N/m}^2 \), what is the elongation?