Question

Two identical billiard balls undergo an oblique elastic collision. Initially, one of the balls is stationary. If the initially stationary ball after collision moves in a direction which makes an angle of 37${}^o$ with direction of initial motion of the moving ball, then the angle through which initially moving ball will be deflected is :

• A. ${37}^o$
• B. ${60}^o$
• C. ${53}^o$
• D. $>{53}^o$

Answer 1

The correct option is C ${53}^o$

Initially, $A$ is moving with velocity $u$ horizontally, collides with stationary ball $B$ making an angle $\theta ={37}^o$ with the horizontal.

Initial velocity of $A$ along $LOC$ $=ucos{37}^o$

Initial velocity of $A$ perpendicular to $LOC$ $=usin{37}^o$

As the two identical particle after perfectly elastic collision exchange their velocities along $LOC$

Thus after collision, velocity of $A$ along $LOC$ $=0$

After collision, velocity of $B$ along $LOC$ $=ucos{37}^o$

But velocity of $A$ perpendicular to $LOC$ remains the same even after the collision, thus it fly off in direction perpendicular to $LOC$

$\therefore$ Angle of deflection of $A$, $\varphi =90-{37}^o={53}^o$