NEET Mechanical Properties of Solids — Set 7

Question 1

A brass block of dimensions $ 0.6 \, \text{m} \times 0.4 \, \text{m} \times 0.2 \, \text{m} $ is subjected to a shearing force of $ 9 \times 10^4 \, \text{N} $. If the shear modulus of brass is $ 3.6 \times 10^{10} \, \text{N/m}^2 $, what is the shear strain?

Accepted Answer

Shear modulus: $ G = \frac{\text{Shear stress}}{\text{Shear strain}} $. Shear stress: $ \text{Shear stress} = \frac{F}{A} $, $ A = 0.6 \times 0.4 = 0.24 \, \text{m}^2 $. Shear stress: $ \frac{9 \times 10^4}{0.24} = 3.75 \times 10^5 \, \text{N/m}^2 $. Shear strain: $ \text{Shear strain} = \frac{\text{Shear stress}}{G} = \frac{3.75 \times 10^5}{3.6 \times 10^{10}} \approx 1.04 \times 10^{-5} $.

Question 2

A steel wire of length $ 2.7 \, \text{m} $ and cross-sectional area $ 2 \times 10^{-6} \, \text{m}^2 $ is stretched by $ 0.54 \, \text{mm} $. If the Young's modulus of steel is $ 2 \times 10^{11} \, \text{N/m}^2 $, what is the stress?

Accepted Answer

Strain: $ \text{Strain} = \frac{\Delta L}{L} = \frac{0.54 \times 10^{-3}}{2.7} = 2 \times 10^{-4} $. Young's modulus: $ Y = \frac{\text{Stress}}{\text{Strain}} $. Stress: $ \text{Stress} = Y \times \text{Strain} = 2 \times 10^{11} \times 2 \times 10^{-4} = 4 \times 10^7 \, \text{N/m}^2 $.

Question 3

A rectangular slab of length 0.4 m, width 0.2 m, and thickness 0.1 m is subjected to a shearing force of 8 × 10 4 N. If the shear modulus is 4 × 10 9 N/m 2 , what is the displacement of the upper face relative to the lower face?

Accepted Answer

Shear modulus: G = (Shear stress) / (Shear strain) = (F / A) / (Δx / L). Rearrange: Δx = (F L) / (A G). Area A = 0.4 × 0.2 = 0.08 m 2 , L = 0.1 m. Substitute: Δx = (8 × 10 4 × 0.1) / (0.08 × 4 × 10 9 ) = 8000 / (3.2 × 10 8 ) = 2.5 × 10 -5 m.

NEET Physics: Mechanical Properties of Solids — Practice Set 7

Q1. A brass block of dimensions \( 0.6 \, \text{m} \times 0.4 \, \text{m} \times 0.2 \, \text{m} \) is subjected to a shearing force of \( 9 \times 10^4 \, \text{N} \). If the shear modulus of brass is \( 3.6 \times 10^{10} \, \text{N/m}^2 \), what is the shear strain?

Q2. A steel wire of length \( 2.7 \, \text{m} \) and cross-sectional area \( 2 \times 10^{-6} \, \text{m}^2 \) is stretched by \( 0.54 \, \text{mm} \). If the Young's modulus of steel is \( 2 \times 10^{11} \, \text{N/m}^2 \), what is the stress?

Q3. A rectangular slab of length 0.4 m, width 0.2 m, and thickness 0.1 m is subjected to a shearing force of 8 × 10 4 N. If the shear modulus is 4 × 10 9 N/m 2 , what is the displacement of the upper face relative to the lower face?

Q4. A steel cable of radius 0.015 m is used to support a load. If the maximum stress it can withstand is 2 × 10 8 N/m 2 , what is the maximum load it can support? (Take π ≈ 3.14)

Q5. An aluminium block of dimensions \( 0.6 \, \text{m} \times 0.4 \, \text{m} \times 0.2 \, \text{m} \) is subjected to a shearing force of \( 8 \times 10^4 \, \text{N} \). If the shear modulus of aluminium is \( 2.5 \times 10^{10} \, \text{N/m}^2 \), what is the displacement of the top face?

Q6. A copper wire of length \( 2.3 \, \text{m} \) 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 copper is \( 1.1 \times 10^{11} \, \text{N/m}^2 \), what is the strain?

Q7. A copper wire of length \( 2.4 \, \text{m} \) and cross-sectional area \( 2 \times 10^{-6} \, \text{m}^2 \) is stretched by a force producing a strain of \( 1.5 \times 10^{-4} \). If the Young's modulus of copper is \( 1.1 \times 10^{11} \, \text{N/m}^2 \), what is the stress?

Q8. A water sample of volume \( 1 \, \text{litre} \) is compressed by a pressure of \( 1 \times 10^6 \, \text{N/m}^2 \). If the bulk modulus of water is \( 2.2 \times 10^9 \, \text{N/m}^2 \), what is the fractional change in volume?

Q9. A copper wire of length \( 2.0 \, \text{m} \) and cross-sectional area \( 2.5 \times 10^{-6} \, \text{m}^2 \) is stretched by a force of \( 250 \, \text{N} \). If the Young's modulus of copper is \( 1.1 \times 10^{11} \, \text{N/m}^2 \), what is the elongation?

Q10. What does the steepness of the linear portion of a stress-strain curve typically indicate about a material?