Question

A spherical ball A of mass $4kg$, moving in a straight line strikes (elastically) another spherical ball B of mass $1kg$ at rest. After the collision, balls A and B move with velocities $V_1$ m/s and $V_2$ m/s 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

$\frac{\sqrt{3}}{4}$

In elastic collision
Momentum is conserved and Kinetic Energy is conserved.

Momentum conserved in $x$ and $y$ direction:
$P_{x_i}=P_{x_f}$
and $P_{y_i}=P_{y_f}{P}_{y_i}=P_{y_f}4\times 0+1\times 0=4v_1\sin {30}^{\circ }-v_2\sin {60}^{\circ }{v}_2\times \frac{\sqrt{3}}{2}=4v_1\times \frac{1}{2}\frac{v_1}{v_2}=\frac{\sqrt{3}}{4}$