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

Answer 1

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
$p_r=\sqrt{p^2+P^2}=\sqrt{(mv{)}^2+(MV{)}^2}$
Which is choice (a), the angle which the resultant momentum $p_r$ subtends with the x-axis is given by
$tan\theta =\frac{P}{p}=\frac{MV}{mv}$, which is choice (b).
Loss of KE = $(\frac{1}{2}m{v}^2+\frac{1}{2}M{V}^2)-\left[\frac{1}{2}\frac{m^2{v}^2+M^2{V}^2}{(M+m)}\right]$
=$\frac{1}{2}\frac{Mm}{(M+m)}(V^2+v^2)$, which is choice (c).
Hence the correct choice is (d).