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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) m1v1^2 = m2v2^2
2. (b) m1v1^2 / m2v2^2 = p1^2 / p2^2
3. (c) m2 / m1 = 4 x p2^2 / p1^2
4. (d) m1 / m2 = 1 / 4

Correct answer: (c) m2 / m1 = 4 x p2^2 / p1^2

Solution

Using the principle of conservation of energy, the relationship between mass, velocity, and momentum can be derived. Since momentum p = mv, the ratio of masses and momenta leads to the given expression m2/m1 = 4 × (p2^2 / p1^2).

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