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If particle takes \( t \) seconds less and acquires a velocity of \( \mathrm{v} \mathrm{m} / \mathrm{s} \) more in falling through the same distance on to planets where the acceleration due to gravity are \( 2 g \) and \( 8 g \) respectively, then

1. \( v=4 g t \)
2. \( v=5 g t \)
3. \( v=2 g t \)
4. \( v=16 g t \)

Correct answer: \( v=4 g t \)

Solution

For the same falling distance, time is inversely related to the square root of gravity, and final speed is proportional to the square root of gravity. Comparing the cases for 2g and 8g gives a speed difference tied to the time difference, leading to v = 4gt.

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