Question

A rectangular metallic block of size \( 40 \, \text{mm} \times 20 \, \text{mm} \) is pulled with a force of \( 50 \, \text{kN} \). The strain in the block is:
(Shear modulus \( = 40 \times 10^9 \, \text{Nm}^{-2} \))

• A. \( 1.56 \times 10^{-3} \, \text{m} \)
• B. \( 2.4 \times 10^{-3} \, \text{m} \)
• C. \( 3.2 \times 10^{-3} \, \text{m} \)
• D. \( 1.08 \times 10^{-3} \, \text{m} \)

Hint:

Use \( \text{strain} = \frac{\text{stress}}{\text{modulus}} \) and convert dimensions to meters when calculating area.

Answer 1

The Correct Option is A

Strain = \( \frac{\text{Stress}}{\text{Modulus}} = \frac{F/A}{\eta} \)
\[ F = 50 \times 10^3 \, \text{N}, \quad A = 40 \times 10^{-3} \cdot 20 \times 10^{-3} = 8 \times 10^{-4} \, \text{m}^2 \Rightarrow \text{Stress} = \frac{50 \times 10^3}{8 \times 10^{-4}} = 6.25 \times 10^7 \]
\[ \text{Strain} = \frac{6.25 \times 10^7}{40 \times 10^9} = 1.56 \times 10^{-3} \]