First slide

Elastic behaviour of solids

Question

The length of a rod is 20 cm and area of cross-section 2 cm². The Young's modulus of the material of wire is $1.4 \times 10^{11} N / m^{2}$ . If the rod is compressed by 5 kg-wt along its length, then increase in the energy of the rod in joules will be

Moderate

A

$8.57 \times 10^{- 6}$
B

$22.5 \times 10^{- 4}$
C

$9.8 \times 10^{- 5}$
D

$45.0 \times 10^{- 5}$

Solution

$\begin{matrix} Energy = \frac{1}{2} Fl = \frac{1}{2} \times F \times (\frac{FL}{AY}) = \frac{1}{2} \times \frac{F^{2} L}{AY} \\ = \frac{1}{2} \times \frac{(50)^{2} \times 20 \times 10^{- 2}}{2 \times 10^{- 4} \times 1 .4 \times 10^{11}} = 8 .57 \times 10^{- 6} J \end{matrix}$

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