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Question

A body of mass m moving with a velocity v in the x-direction collides and sticks with another body of mass M moving with a velocity V in the y-direction. The magnitude of the momentum of the composite body is


A

(mv+MV)

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B

(m+M)(v+V)

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C

(mv)2+(MV)2

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D

(Mv+mV)

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Solution

The correct option is C

(mv)2+(MV)2



Let v' be the velocity of the composite body at an angle θ with the x-axis as shown in the figure. Equating the initial and the final momentum along x and y-axis,
mv=(m+M)v cos θ=P cos θ .... (i)
and MV=(m+M)v sin θ=P sin θ .... (ii)
where P=(m+M)v is the momentum of the composite body. Squaring and adding equations (i) and (ii),
(P)2=(mv)2+(MV)2P=(mv)2+(MV)2
Hence, the correct choice is (c).


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