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Question

A body of mass 'm' moving with a velocity 'v' in the x-direction collides with a body of mass 'M' moving with a velocity 'V' in the y-direction. They stick together during a collision. Then

A
The magnitude of the momentum of the composite body is
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B
The composite body moves in a direction making a angle with the x-axis.
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C
The loss of kinetic energy as a result of collision is
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D
All the above choices are correct.
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Solution

The correct option is D All the above choices are correct.
Refer to Figure Here p = mv and P = MV.

The resultant of p and P is
pr=p2+P2=(mv)2+(MV)2
Which is choice (a), the angle which the resultant momentum pr subtends with the x-axis is given by
tanθ=Pp=MVmv, which is choice (b).
Loss of KE = (12mv2+12MV2)[12m2v2+M2V2(M+m)]
=12Mm(M+m)(V2+v2), which is choice (c).
Hence the correct choice is (d).

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