NEET Mechanical Properties of Solids — Set 6

Question 1

An aluminium rod of length $ 1.4 \, \text{m} $ and cross-sectional area $ 2 \times 10^{-6} \, \text{m}^2 $ is compressed by a force producing a stress of $ 3 \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 compression?

Accepted Answer

Young's modulus: $ Y = \frac{\text{Stress}}{\text{Strain}} $. Strain: $ \text{Strain} = \frac{\text{Stress}}{Y} = \frac{3 \times 10^7}{7 \times 10^{10}} \approx 4.29 \times 10^{-4} $. Compression: $ \Delta L = \text{Strain} \times L = 4.29 \times 10^{-4} \times 1.4 \approx 6 \times 10^{-4} \, \text{m} = 0.6 \, \text{mm} $.

Question 2

A steel wire of length $ 2.7 \, \text{m} $ and cross-sectional area $ 3 \times 10^{-6} \, \text{m}^2 $ is stretched by a force of $ 450 \, \text{N} $. If the Young's modulus of steel is $ 2 \times 10^{11} \, \text{N/m}^2 $, what is the strain?

Accepted Answer

Stress: $ \text{Stress} = \frac{F}{A} = \frac{450}{3 \times 10^{-6}} = 1.5 \times 10^8 \, \text{N/m}^2 $. Young's modulus: $ Y = \frac{\text{Stress}}{\text{Strain}} $. Strain: $ \text{Strain} = \frac{\text{Stress}}{Y} = \frac{1.5 \times 10^8}{2 \times 10^{11}} = 7.5 \times 10^{-4} $.

Question 3

A copper block of dimensions $ 0.6 \, \text{m} \times 0.4 \, \text{m} \times 0.2 \, \text{m} $ is subjected to a shearing force of $ 7 \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?

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{7 \times 10^4}{0.24} \approx 2.92 \times 10^5 \, \text{N/m}^2 $. Shear strain: $ \text{Shear strain} = \frac{\text{Shear stress}}{G} = \frac{2.92 \times 10^5}{4.2 \times 10^{10}} \approx 6.95 \times 10^{-6} $.

NEET Physics: Mechanical Properties of Solids — Practice Set 6

Q2. A steel wire of length \( 2.7 \, \text{m} \) and cross-sectional area \( 3 \times 10^{-6} \, \text{m}^2 \) is stretched by a force of \( 450 \, \text{N} \). If the Young's modulus of steel is \( 2 \times 10^{11} \, \text{N/m}^2 \), what is the strain?

Q3. A copper block of dimensions \( 0.6 \, \text{m} \times 0.4 \, \text{m} \times 0.2 \, \text{m} \) is subjected to a shearing force of \( 7 \times 10^4 \, \text{N} \). If the shear modulus of copper is \( 4.2 \times 10^{10} \, \text{N/m}^2 \), what is the shear strain?

Q4. A steel wire of length 2 m and cross-sectional area 2 × 10 -6 m 2 is stretched by a force of 200 N. If the Young's modulus of steel is 2 × 10 11 N/m 2 , what is the elongation of the wire?

Q5. What is the key difference between elastic and plastic deformation in a material?

Q6. A steel cable of radius 0.02 m is used to lift a load. If the maximum stress it can withstand is 1 × 10 8 N/m 2 , what is the maximum load it can support? (Take π ≈ 3.14)

Q7. A glass slab experiences a hydraulic pressure of 8 × 10 6 N/m 2 . If the bulk modulus of glass is 3.7 × 10 10 N/m 2 , what is the fractional change in volume?

Q8. A steel wire of length 5 m and cross-sectional area 4 × 10 -6 m 2 is stretched by 0.5 mm. If the Young's modulus of steel is 2 × 10 11 N/m 2 , what is the stress?

Q9. A brass block of dimensions \( 0.5 \, \text{m} \times 0.3 \, \text{m} \times 0.2 \, \text{m} \) is subjected to a shearing force of \( 6 \times 10^4 \, \text{N} \). If the shear modulus of brass is \( 3.6 \times 10^{10} \, \text{N/m}^2 \), what is the displacement of the top face?

Q10. Which modulus describes a material’s resistance to volume change under uniform pressure in all directions?