Question

A ball moving with a speed of $9m{s}^{-1}$ strikes an identical stationary ball such that after the collision the direction of each ball makes an angle of ${30}^0$ with the original line of motion. The speed of two balls after the collision is:

• A. $3m{s}^{-1}$, $3m{s}^{-1}$
• B. $3\sqrt{3}m{s}^{-1}$, $3\sqrt{3}m{s}^{-1}$
• C. $3\sqrt{3}m{s}^{-1}$, $3m{s}^{-1}$
• D. $3m{s}^{-1}$, $3\sqrt{3}m{s}^{-1}$

Answer 1

The correct option is B $3\sqrt{3}m{s}^{-1}$, $3\sqrt{3}m{s}^{-1}$

Applying conservation of linear momentum in the direction perpendicular to the initial velocity :

$m{v}_{1}sin60°-m{v}_{2}sin60°=0$

$v_1=v_2$

Applying conservation of linear momentum in the direction of initial velocity of the first ball :

$mu=m{v}_{1}cos30°+m{v}_{2}cos30°$

$9=2vcos30=2\surd 3v$

$⟹v=3\surd 3m{s}^{-1}$