NEET Mechanical Properties of Solids — Set 3

Question 1

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

Accepted Answer

The tight coupling between neighboring atoms in solids results in a much higher resistance to volume change compared to gases, where molecules are weakly coupled.

Question 2

A brass wire of length 1.5 m and cross-sectional area 2.5 × 10 -6 m 2 is stretched by a force of 150 N. If the elongation is 0.25 mm, what is the Young's modulus of brass?

Accepted Answer

Young's modulus: Y = (F L) / (A ΔL). Substitute: ΔL = 0.25 × 10 -3 m. Y = (150 × 1.5) / (2.5 × 10 -6 × 0.25 × 10 -3 ) = 225 / (6.25 × 10 -10 ) = 3.6 × 10 11 N/m 2 .

Question 3

A water sample of volume $ 2.5 \, \text{litres} $ is compressed by a pressure of $ 2 \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{2 \times 10^6}{2.2 \times 10^9} \approx -9.09 \times 10^{-4} $. Magnitude: $ 9.09 \times 10^{-4} $.

NEET Physics: Mechanical Properties of Solids — Practice Set 3

Q1. What is the primary reason solids are far less compressible than gases?

Q2. A brass wire of length 1.5 m and cross-sectional area 2.5 × 10 -6 m 2 is stretched by a force of 150 N. If the elongation is 0.25 mm, what is the Young's modulus of brass?

Q3. A water sample of volume \( 2.5 \, \text{litres} \) is compressed by a pressure of \( 2 \times 10^6 \, \text{N/m}^2 \). If the bulk modulus of water is \( 2.2 \times 10^9 \, \text{N/m}^2 \), what is the fractional change in volume?

Q4. An aluminium wire of length \( 2.3 \, \text{m} \) and cross-sectional area \( 1.5 \times 10^{-6} \, \text{m}^2 \) is stretched by a force producing a stress of \( 2 \times 10^7 \, \text{N/m}^2 \). If the Young's modulus of aluminium is \( 7 \times 10^{10} \, \text{N/m}^2 \), what is the strain?

Q5. A glass slab of volume \( 0.02 \, \text{m}^3 \) 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 fractional change in volume?

Q6. A glass block of volume 0.01 m 3 is subjected to a hydraulic pressure of 4 × 10 6 N/m 2 . If the bulk modulus of glass is 3.7 × 10 10 N/m 2 , what is the change in volume?

Q7. A brass wire of length \( 2.0 \, \text{m} \) and cross-sectional area \( 2 \times 10^{-6} \, \text{m}^2 \) is stretched by a force of \( 300 \, \text{N} \). If the Young's modulus of brass is \( 9 \times 10^{10} \, \text{N/m}^2 \), what is the strain produced?

Q8. A copper cube of edge length 0.1 m is subjected to a hydraulic pressure of 5 × 10 6 N/m 2 . If the bulk modulus of copper is 1.4 × 10 11 N/m 2 , what is the change in volume?

Q9. A copper wire of length 2 m and cross-sectional area 2 × 10 -6 m 2 is stretched by a force of 200 N. If the elongation is 0.727 mm, what is the Young's modulus of copper?

Q10. A steel wire of length \( 1.5 \, \text{m} \) and cross-sectional area \( 1 \times 10^{-6} \, \text{m}^2 \) is stretched by a force of \( 100 \, \text{N} \). If the Young's modulus of steel is \( 2 \times 10^{11} \, \text{N/m}^2 \), what is the elongation?