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Initial momentum (p1) = p; Final momentum (p2) = 1.5 p and initial kinetic energy (K1) = K.

1. (a) Kinetic energy (K) = p^2 / 2m ∝ p^2
2. (b) K1 / K2 = (p1 / p2)^2 = p / 1.5p = 1 / 2.25
3. (c) K2 = 2.25 K
4. (d) Increase in kinetic energy is 2.25 K - K = 1.25 K or 125%

Correct answer: (c) K2 = 2.25 K

Solution

The kinetic energy is proportional to the square of momentum (K ∝ p²). If the final momentum is 1.5p, then K2 = (1.5p)² / 2m = 2.25K. Thus, option (c) is correct.

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