First slide

Simple hormonic motion

Question

A spring when stretched up to 2 cm has potential energy U. If it is stretched up to 10 cm, potential energy would be

Easy

A

U /25
B

U/5
C

5 U
D

25U

Solution

$The potential energy U_{p} of spring is given by U_{p} = \frac{1}{2} {kx}^{2} In first case, U = \frac{1}{2} k (2)^{2} = 2 k or k = U / 2 In second case, U_{p} = \frac{1}{2} k (10)^{2} = \frac{1}{2} \times \frac{U}{2} \times (10)^{2} = 25 U$

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