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Two particles, each of mass m, move with initial velocities u*i and u*(i + j)/2 respectively. They undergo a perfectly inelastic collision and stick together. How much kinetic energy is lost?

1. 3/4 mu²
2. 1/8 mu²
3. sqrt(2/3) mu²
4. 1/3 mu²

Correct answer: 1/8 mu²

Solution

The relative velocity is u*(i+j)/2 - u*i = u*(-i+j)/2 with magnitude u/sqrt(2); using reduced mass m/2 gives loss = (1/2)(m/2)(u²/2) = mu²/8.

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