The potential energy of a long spring when stretched by 2 cm is . If the spring is stretched by 8 cm, the potential energy stored in it will be: [2023]

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Solution

Q.
The potential energy of a long spring when stretched by 2 cm is $U$ . If the spring is stretched by 8 cm, the potential energy stored in it will be: [2023]

1 8 $U$

2 16 $U$

3 2 $U$

4 4 $U$

Ans.
(2)

Potential energy when spring is stretched by 2 cm is

$U = \frac{1}{2} k x^{2} = \frac{1}{2} k {(2)}^{2} = 2 k$ ...(i)

Potential energy when spring is stretched by 8 cm is

$U' = \frac{1}{2} k {(8)}^{2} = 32 k$ ...(ii)

From eqn (i) and (ii), we get

$∴$ $\frac{U'}{U} = \frac{32 k}{2 k} = 16 \Rightarrow U' = 16 U$

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