When a steel rod of length 2m is compressed its length decreases by 0.1cm. Find the work done per unit volume against the compressive stress.
(Y_steel = 2.0 × 10¹¹Nm^–2)

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1.25 x 10⁴ J m^-3

7.5 x 10⁴ J m^-3

5.0 x 10⁴ J m^-3

2.5 x 10⁴ J m^-3

answer is A.

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Detailed Solution

l = 2m, e = 1 x 10^-3 m, y = 2 x 10¹¹ N/m²
$\frac{w}{v} = \frac{1}{2} y \frac{e^{2}}{l^{2}} = \frac{\frac{1}{2} x 2 x 10^{11} x 1 x 10^{6}}{4}$
w = 0.25 x 10⁵ J $\Rightarrow$ 2.5 x 10⁴ J

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