A spring with spring constant $K$ when stretched through $2 c m$ the potential energy is $U$ . If it is stretched by $6 c m$ . The potential energy will be

6 U

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3 U

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9 U

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18 U

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Solution

The correct option is C $9 U$
PE of the spring $α x^{2}$

$\Rightarrow$ $\frac{P E_{1}}{P E_{2}} =$ $\frac{2^{2}}{6^{2}} =$ $\frac{1}{9}$
$\Rightarrow P E_{2} = 9 \times P E_{1} = 9 U$

Hence correct answer is option $C$

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