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  4. A long spring, when stretched by a distance x, has potential energy U. On increasing the stretching to rue, the potential energy of the spring will be

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Q. A long spring, when stretched by a distance x, has potential energy U. On increasing the stretching to rue, the potential energy of the spring will be

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Solution:

Potential energy of the spring $ U=\frac{1}{2}k\,{{x}^{2}} $ ?(i) and $ U=\frac{1}{2}k{{(nx)}^{2}} $ $ \Rightarrow $ $ U={{n}^{2}}\frac{1}{2}k\,{{x}^{2}} $ $ \therefore $ $ U={{n}^{2}}U $ [From Eq. (i)]