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Question

Two bodies A and B having masses m and 4m respectively are moving with equal linear momentum. The ratio of kinetic energies between A and B is _________.

A
1 : 4
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B
4 : 1
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C
1 : 1
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D
1 : 2
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Solution

The correct option is C 1 : 4
Let M1 and M2 be momentum of the two bodies moving with velocities v1 and v2 resp.
Now M= m×v
For A: M1 = m1×v1 = m×v1
For B: M2 = m2×v2 = 4m×v2

But M1 = M2
v1v2 = 14
KE1 = 12×m1×v21
= 12×m1×v1×v1

= 12×M1×v1

KE2 = 12×m2×v22
= 12×m2×v2×v1

= 12×M2×v2

Hence, KE1KE2 = v1v2 = 14

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