Question

A smooth sphere $A$ of mass $m$ collides elastically with an identical sphere $B$ at rest. The velocity of $A$ before collision is $8\text{m/s}$ in a direction making ${60}^{\circ }$ with the line joining the centres at the time of impact.
Which of the following is/are possible:

• A. the sphere $A$ comes to rest after collision
• B. the sphere $B$ will move with a speed of $8\text{m/s}$ after collision
• C. the direction of motion of $A$ and $B$ after collision are at right angles
• D. the speed of $B$ after collision is $4\text{m/s}$

Answer 1

Answer: (C), (D)

the speed of $B$ after collision is $4\text{m/s}$

Sphere $A$ moving with velocity $v$ has a component $v/2$ along the line joining the centres of the spheres at the time of collision and another component $v\sqrt{3}/2$ perpendicular to the previous direction. After collision the component along the line will interchange i.e B will move with $v/2$ velocity i,e $4\text{m/s}$ along the line joining the centres and $A$ moves with $v\sqrt{3}/2$ velocity at perpendcular direction to $B$.