NEET Mechanical Properties of Solids — Set 15

Question 1

A brass block of dimensions $ 0.4 \, \text{m} \times 0.3 \, \text{m} \times 0.1 \, \text{m} $ is subjected to a shearing force of $ 3 \times 10^4 \, \text{N} $. If the shear modulus of brass is $ 3.6 \times 10^{10} \, \text{N/m}^2 $, what is the displacement of the top face?

Accepted Answer

Shear modulus: $ G = \frac{F / A}{\Delta x / L} $. Rearrange: $ \Delta x = \frac{F L}{A G} $. Area: $ A = 0.4 \times 0.3 = 0.12 \, \text{m}^2 $, $ L = 0.1 \, \text{m} $. Substitute: $ \Delta x = \frac{3 \times 10^4 \times 0.1}{0.12 \times 3.6 \times 10^{10}} = \frac{3000}{4.32 \times 10^9} \approx 6.94 \times 10^{-7} \, \text{m} $.

Question 2

Which type of stress causes a change in the shape of a body without altering its volume?

Accepted Answer

Shearing stress causes a change in the shape of a body by producing relative displacement of opposite faces (pure shear) without changing its volume.

Question 3

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

Accepted Answer

A ductile material undergoes significant plastic deformation before fracture, allowing it to withstand larger strains, while a brittle material fractures with minimal plastic deformation.

NEET Physics: Mechanical Properties of Solids — Practice Set 15

Q1. A brass block of dimensions \( 0.4 \, \text{m} \times 0.3 \, \text{m} \times 0.1 \, \text{m} \) is subjected to a shearing force of \( 3 \times 10^4 \, \text{N} \). If the shear modulus of brass is \( 3.6 \times 10^{10} \, \text{N/m}^2 \), what is the displacement of the top face?

Q2. Which type of stress causes a change in the shape of a body without altering its volume?

Q3. What distinguishes a ductile material from a brittle material in terms of stress-strain behavior?

Q4. A water sample of volume \( 3 \, \text{litres} \) is compressed by a pressure of \( 4 \times 10^6 \, \text{N/m}^2 \). If the bulk modulus of water is \( 2.2 \times 10^9 \, \text{N/m}^2 \), what is the change in volume?

Q5. A rectangular block of aluminium with dimensions 0.5 m × 0.2 m × 0.1 m is subjected to a shearing force of 6 × 10 4 N. If the shear modulus of aluminium is 2.5 × 10 10 N/m 2 , what is the shear strain?

Q6. In the stress-strain behavior of a ductile material, what happens after the maximum stress the material can endure?

Q7. A brass block of dimensions \( 0.5 \, \text{m} \times 0.2 \, \text{m} \times 0.05 \, \text{m} \) is subjected to a shearing force of \( 2 \times 10^4 \, \text{N} \). If the shear modulus of brass is \( 3.6 \times 10^{10} \, \text{N/m}^2 \), what is the shear strain?

Q8. An aluminium wire of length \( 1.8 \, \text{m} \) 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 aluminium is \( 7 \times 10^{10} \, \text{N/m}^2 \), what is the force applied?

Q9. A steel block of dimensions 0.2 m × 0.1 m × 0.05 m is subjected to a shearing force of 1 × 10 4 N. If the shear modulus of steel is 8.4 × 10 10 N/m 2 , what is the shear strain?

Q10. In the stress-strain behavior of a material, what occurs after the maximum stress point when the material is ductile?