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
√(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)2⇒P′=√(mv)2+(MV)2
Hence, the correct choice is (c).