First slide

Work done by Diff type of forces

Question

Work done by an external agent in stretching a spring by 1 cm is 9 J, work done in stretching the same spring by 2 cm is 16 J. Then the work done in stretching the same spring by 3 cm is

Moderate

A

24 J
B

25 J
C

32 J
D

50 J

Solution

$W_{1} = \frac{1}{2} K x^{2} \Rightarrow x = \sqrt{\frac{2 W_{1}}{K}} a n d y = \sqrt{\frac{2 W_{2}}{K}}$
$W = \frac{1}{2} K {(x + y)}^{2} = \frac{1}{2} K {[\sqrt{\frac{2 W_{1}}{K}} + \sqrt{\frac{2 W_{2}}{K}}]}^{2}$
$= {(\sqrt{W_{1}} + \sqrt{W_{2}})}^{2} = {(\sqrt{4} + \sqrt{9})}^{2} J = 25 J$

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