Question

A sphere of mass `m`, impinges obliquely on a sphere, of mass M, which is at rest. Show that, if `m=eM`, the directions of motion of the sphere after impact are at right angles.

Answer 1

Let CT stands for common tangent direction and CN for common normal direcitons.
In the common tangent directions velocity components remain unchanged.
In common normal direction applying conservation of linear momentum and definition of `e`,
`eMv_2=eMv_3+Mv_4` ...(i)
From the definition of coefficient of restitution
`e=(v_4-v_3)/(v_2)` ...(ii)
Solving these two equations we get,
`v_3=0` but `v_4!=0`
So, after collision velocity of m is along CT while that of M along CN or they are moving at right angles.