Question

The lower edge of a square slab of side $50$ cm and thickness $20$ cm is rigidly fixed to the base of a table. A tangential force of $30$ N is applied to the slab. If the shear modulus of the material is $4 \times 10^{10}$ N/m$^2$, then displacement of the upper edge, in meters, is}

• A. $4 \times 10^{-12}$
• B. $4 \times 10^{-10}$
• C. $6 \times 10^{-10}$
• D. $6 \times 10^{-12}$
• E. $8 \times 10^{-10}$

Hint:

Always identify area perpendicular to force when calculating stress.

Answer 1

The Correct Option is C

Concept:
\[ G = \frac{\text{Stress}}{\text{Strain}} = \frac{F/A}{x/L} \Rightarrow x = \frac{F L}{A G} \]

Step 1: Convert units.
\[ L = 0.2 \text{ m}, \quad A = (0.5)^2 = 0.25 \text{ m}^2 \]

Step 2: Substitute values.
\[ x = \frac{30 \times 0.2}{0.25 \times 4 \times 10^{10}} \]

Step 3: Calculate.
\[ x = \frac{6}{10^{10}} = 6 \times 10^{-10} \]