Question

A spherical ball $A$ of mass $4kg$, moving along a straight line strikes another spherical ball $B$ of mass $1kg$ at rest. After the collision, $A$ and $B$ move with velocities $v_{1}m{s}^{-1}$ and $v_{2}m{s}^{-1}$ respectively making angles of ${30}^{\circ }$ and ${60}^{\circ }$ with respect to the original direction of motion of $A$. The ratio $\frac{v_1}{v_2}$ will be:

• A. $\frac{\sqrt{3}}{4}$
• B. $\frac{4}{\sqrt{3}}$
• C. $\frac{1}{\sqrt{3}}$
• D. $\sqrt{3}$

Answer 1

The correct option is A $\frac{\sqrt{3}}{4}$

Applying the law of conservation of linear momentum along a direction perpendicular to the direction of motion (i.e. along y-axis), we get
$0+0=4v_1\sin {30}^{\circ }-v_2\sin {60}^{\circ }$
$4v_1\sin {30}^{\circ }=v_2\sin {60}^{\circ }$ or

$\frac{v_1}{v_2}=\frac{\sin {60}^{\circ }}{4\sin {30}^{\circ }}=\frac{\sqrt{3}}{4}$.