Ncert Exercises & Solutions

9.6 The edge of an aluminium cube is 10 cm long. One face of the cube is firmly fixed to a vertical wall. A mass of 100 kg is then attached to the opposite face of the cube. The shear modulus of aluminium is 25 GPa. What is the vertical deflection of this face?

Hint: Recall the expression for shear modulus.

Step 1: The expression for shear modulus is:

$η = \frac{F \times L}{A \times ∆ L} .$

Step 2: Calculate vertical deflection by rearranging the above expression.

$As, η = \frac{F \times L}{A \times ∆ L}$
$So, Vertical deflection = ∆ L = \frac{m \times g \times L}{A \times η}$
$∆ L = \frac{100 \times 9.8 \times 0.1}{0.1 \times 0.1 \times 25 \times 10^{9}}$
$∆ L = 3.92 \times 10^{- 7} m .$

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