First slide

Elastic behaviour of solids

Question

A long elastic spring is stretched by 2 cm and its potential energy is U. If the spring is stretched by 10 cm, the P.E., will be

Moderate

A

5 U
B

25 U
C

U/5
D

U/20

Solution

The elastic potential is
$Energy = \frac{1}{2} Stress \times Strain$
$\begin{array}{l} = \frac{1}{2} Y (strain)^{2} = \frac{1}{2} Y {(\frac{Δl}{L})}^{2} \\ ∴ \frac{U_{2}}{U_{1}} \propto {(\frac{{Δl}_{2}}{{Δl}_{1}})}^{2} = {(\frac{10}{2})}^{2} \\ \frac{U_{2}}{U_{1}} = 25 \Rightarrow U_{2} = 25 U_{1} = 25 U [U_{1} = U] \end{array}$

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