First slide

Elastic Modulie

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

$\frac{U}{5}$
D

$\frac{U}{20}$

Solution

The elastic pot. Energy = $\frac{1}{2} stress \times strain .$
= $\frac{1}{2} Y {(strain)}^{2} = \frac{1}{2} Y {(\frac{∆ L}{L})}^{2}$
$\frac{U_{2}}{U_{1}} \infty {(\frac{∆ l_{2}}{∆ l_{1}})}^{2} = {(\frac{10}{2})}^{2}$
$\frac{U_{2}}{U} = 25$
$\Rightarrow U_{2} = 25 U_{}$
So the correct choice is (2).

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