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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 is

1. 8U
2. 16U
3. U/4
4. 4U

Correct answer: 16U

Solution

The potential energy stored in a spring is proportional to the square of the extension (U ∝ x²). If the extension increases from 2 cm to 8 cm, the ratio of extensions is 8/2 = 4. Squaring this gives 4² = 16, so the potential energy becomes 16U.

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