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A stone is dropped from a height h. It hits the ground with a certain momentum P. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by:

1. 68%
2. 41%
3. 200%
4. 100%

Correct answer: 68%

Solution

The momentum of the stone is proportional to the square root of the height (P ∝ √h). If the height is increased by 100%, the new height becomes 2h, and the new momentum becomes √2 times the original momentum. The percentage change in momentum is [(√2 - 1) / 1] × 100 ≈ 41%.

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