A ball will a speed of $9 \mathrm{~m} / \mathrm{s}$ collides with another identical ball at rest. After the collision, the direction of each ball makes an angle of $30^{\circ}$ with the original direction. The ratio of velocities of the balls after collision is $\mathrm{x}: \mathrm{y}$, where $x$ is
From conservation of momentum along $y$-axis.
$\vec{P}_{i y}=\vec{P}_{f y}$
$0+0=m v_{1} \sin 30^{\circ} \hat{\mathrm{j}}+\mathrm{mv}_{2} \sin 30^{\circ}(-\hat{\mathrm{j}})$
$\mathrm{mv}_{2} \sin 30^{\circ}=\mathrm{mv}_{1} \sin 30^{\circ}$
$\mathrm{v}_{2}=\mathrm{v}_{1}$ or $\frac{\mathrm{v}_{1}}{\mathrm{v}_{2}}=1$
Ans. 1
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