Question

A ball of mass $10\text{kg}$ moving with a velocity $10\sqrt{3}{\text{ms}}^{-1}$ along $X-$axis, hits another ball of mass $20\text{kg}$ which is at rest. After collision, the first ball comes to rest and the second one disintegrates into two equal pieces. One of the pieces starts moving along $Y-$axis at a speed of $10\text{m/s}$. The second piece starts moving at a speed of $20\text{m/s}$ at an angle $\theta$ (degrees) with respect to the $X-$axis. The configuration of the pieces after collision is shown in the figure. The value of $\theta$ to the nearest integer is .

Answer 1

Conserving momentum along the $X-$axis
${\overrightarrow{\left(p_i\right)}}_x={\overrightarrow{\left(p_f\right)}}_x$
$\Rightarrow 10\times 10\sqrt{3}=10\times 20\cos \theta$
$\Rightarrow \cos \theta =\frac{\sqrt{3}}{2}$
$\Rightarrow \theta ={30}^{\circ }$
$\therefore {30}^{\circ }$ is the required value.