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Question

A moving body with a mass m1 strikes a stationary body of mass m2. The masses of m1 and m2 should be in the ration m1m2 so as to decrease the velocity of the first body 1.5 times assuming a perfectly elastic impact. Then the ratio m1m2 is

A
125
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B
15
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C
5
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D
25
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Solution

The correct option is C 5Here, coefficient of restitution, e is 1.Let initial velocity of mass m1 be v1 and final velocity of mass m2 be v2. According to the question, the final velocity of mass m1 is v1/1.5=2v1/3. So, e=1=(v2−2v1/3)/v1⇒v2=5v1/3 −(1)Now by conservation of momentum, m1v1=m1v1/1.5+m2v2using (1), 5m2v1/3=m1v1/3⇒m1/m2=5

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