Question

A ball with initial speed of $10m/s$ collides elastically with two other identical ball whose centres are on a line perpendicular to the initial velocity and which are initially in contact with each other. All the three ball are lying on a smooth horizontal table. The first ball is aimed directly at the contact point of the other two balls. All the balls are smooth. Find the velocities of the three balls after the collision :

• A. $8m/s,6m/s,\angle {30}^{\circ }$
• B. $-2m/s,6.93m/s,\angle {30}^{\circ }$
• C. $3.33m/s,6.67m/s,\angle {30}^{\circ }$
• D. $6.67m/s,3.33m/s,\angle {30}^{\circ }$

Answer 1

The correct option is B $-2m/s,6.93m/s,\angle {30}^{\circ }$

The collision is symmetric,the two blocks will acquire velocity in direction ${30}^{\circ }$ from horizontal.
writing momentum balance equation in x direction
$m\times 10=m{v}^{\prime }+2mvcos30$...(i)
where $v^{\prime }$ is velocity of block A after collision and $v$ is magnitude of velocity of blocks B and C after collision.
using Kinetic energy conservation

$\frac{1}{2}m{10}^2=2\ast \frac{1}{2}m{v}^2+\frac{1}{2}m{v}^{\prime 2}$...(ii)

solving the equation (i) and (ii)
$v^{\prime }=-2m/s;v=6.93m/s$