First slide

Elastic behaviour of solids

Question

If the potential energy of a spring is V on stretching it by 2 cm, then its potential energy when it is stretched by 10 cm will be

Moderate

A

V/25
B

5V
C

V/5
D

25V

Solution

$\begin{array}{l} U = \frac{1}{2} (\frac{YA}{L}) l^{2} ∴ U \propto l^{2} \\ \frac{U_{2}}{U_{1}} = {(\frac{l_{2}}{l_{1}})}^{2} = {(\frac{10}{2})}^{2} = 25 \Rightarrow U_{2} = 25 U_{1} \end{array}$
i.e., potential energy of the spring will be 25 V.

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