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A body of mass m1 moving with speed v1 collides head-on with another body of mass m2 initially at rest. If the collision is perfectly elastic and the first body’s speed after impact becomes 2v1/3, what must be the ratio m1/m2?

1. 5
2. 1/5
3. 1/25
4. 25

Correct answer: 5

Solution

For an elastic head-on collision with target at rest, v1' = (m1-m2)/(m1+m2) v1. Since the speed stays 2v1/3 in the same direction, (m1-m2)/(m1+m2) = 2/3, giving 3m1-3m2 = 2m1+2m2, so m1 = 5m2, i.e. m1/m2 = 5.

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