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According to principle of conservation of energy, Loss in potential energy = Gain in kinetic energy. If h1 and h2 are initial and final heights, then v1 = √2gh1 and v2 = √2gh2.

1. (a) mgh = 1/2 mv^2 => v = √2gh
2. (b) If h1 and h2 are initial and final heights, then v1 = √2gh1 and v2 = √2gh2
3. (c) Loss in velocity, Δv = v1 - v2 = √2gh1 - √2gh2
4. (d) Fractional loss in velocity, Δv / v1 = √2gh1 - √2gh2 / √2gh1

Correct answer: (b) If h1 and h2 are initial and final heights, then v1 = √2gh1 and v2 = √2gh2

Solution

Option (b) correctly states the relationship between velocity and height derived from the conservation of energy principle, where the potential energy converts into kinetic energy.

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