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A body of mass 4m at rest explodes into three pieces of masses m, m and 2m. The fragments of mass m and 2m fly apart with equal speeds v in opposite directions. What is the total kinetic energy released in the explosion?

1. mv²
2. 2mv²
3. 1/2 mv²
4. 4mv²

Correct answer: 2mv²

Solution

The m and 2m pieces carry momenta mv and 2mv in opposite directions; net of these is mv, so the third m piece moves at v in the opposite direction. Total KE = (1/2)m v² + (1/2)(2m)v² + (1/2)m v² = 2mv².

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