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Question

A stationary object explodes into masses m1 and m2. They move in opposite directions with velocities V1 and V2. The ratio of kinetic energy E1 to kinetic energy E2 is.

A
m2m1
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B
m1m2
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C
2m2m1
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D
2m1m2
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Solution

The correct option is A m2m1
As the initial momentum of the system is zero, thus according to the conservation of linear momentum final momentum of the system must also be zero.
So, magnitude of momentum of mass m1 must be equal to that of mass m2 i.e. m1V1=m2V2 Or p1=p2
Kinetic energy of mass m1, E1=p212m1
Kinetic energy of mass m2, E2=p222m2
Thus ratio of kinetic energy E1E2=p21/2m1p22/2m2 (using p1=p2)
E1E2=m2m1

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