NEET Mechanical Properties of Solids — Set 12

Question 1

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

Accepted Answer

The shear modulus is not applicable for liquids and gases because they do not sustain shear stress and instead flow; only solids have a defined shear modulus.

Question 2

A brass plate experiences a shearing force of 4 × 10 4 N across an area of 0.05 m 2 . If the shear strain is 2 × 10 -5 , what is the shear modulus of brass?

Accepted Answer

Shear modulus: G = (Shear stress) / (Shear strain). Shear stress: Shear stress = F / A = (4 × 10 4 ) / 0.05 = 8 × 10 5 N/m 2 . Shear strain: 2 × 10 -5 . Substitute: G = (8 × 10 5 ) / (2 × 10 -5 ) = 4 × 10 10 N/m 2 .

Question 3

A steel block of dimensions $ 0.5 \, \text{m} \times 0.3 \, \text{m} \times 0.1 \, \text{m} $ is subjected to a shearing force of $ 5 \times 10^4 \, \text{N} $. If the shear modulus of steel is $ 8.4 \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 = 0.5 \times 0.3 = 0.15 \, \text{m}^2 $. Shear stress: $ \frac{5 \times 10^4}{0.15} \approx 3.33 \times 10^5 \, \text{N/m}^2 $. Shear strain: $ \text{Shear strain} = \frac{\text{Shear stress}}{G} = \frac{3.33 \times 10^5}{8.4 \times 10^{10}} \approx 3.96 \times 10^{-6} $.

NEET Physics: Mechanical Properties of Solids — Practice Set 12

Q1. Which modulus is not applicable for describing the elastic behavior of liquids and gases under shear stress?

Q2. A brass plate experiences a shearing force of 4 × 10 4 N across an area of 0.05 m 2 . If the shear strain is 2 × 10 -5 , what is the shear modulus of brass?

Q3. A steel block of dimensions \( 0.5 \, \text{m} \times 0.3 \, \text{m} \times 0.1 \, \text{m} \) is subjected to a shearing force of \( 5 \times 10^4 \, \text{N} \). If the shear modulus of steel is \( 8.4 \times 10^{10} \, \text{N/m}^2 \), what is the shear strain?

Q4. A brass rod of length 2 m and cross-sectional area 5 × 10 -6 m 2 is compressed by a force of 1000 N. If the Young's modulus of brass is 9 × 10 10 N/m 2 , what is the longitudinal strain?

Q5. A steel wire of length \( 2.8 \, \text{m} \) and cross-sectional area \( 3 \times 10^{-6} \, \text{m}^2 \) is stretched by \( 0.7 \, \text{mm} \). If the Young's modulus of steel is \( 2 \times 10^{11} \, \text{N/m}^2 \), what is the strain?

Q6. A copper wire of length \( 2.5 \, \text{m} \) 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 stress?

Q7. A brass wire of length \( 1.9 \, \text{m} \) and cross-sectional area \( 2 \times 10^{-6} \, \text{m}^2 \) 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 force applied?

Q8. A brass wire of length 3 m and cross-sectional area 2 × 10 -6 m 2 is stretched by a force of 400 N. If the Young's modulus of brass is 9 × 10 10 N/m 2 , what is the elongation?

Q9. A brass wire of length \( 1.7 \, \text{m} \) and cross-sectional area \( 2 \times 10^{-6} \, \text{m}^2 \) is stretched by a force producing a strain of \( 4 \times 10^{-4} \). If the Young's modulus of brass is \( 9 \times 10^{10} \, \text{N/m}^2 \), what is the stress?

Q10. What distinguishes a ductile material from a brittle material in terms of stress-strain behavior?