Question 213 of 280

A ball of mass $10kg$ moving with a velocity $10\sqrt{3}{ms}^{-1}$ along $X$-axis, hits another ball of mass $20kg$ which is at rest. After the 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 $10m{s}^{-1}$. The second piece starts moving at a speed of $20m{s}^{-1}$ at an angle $\theta$ (degree) with respect to the $X$-axis. The configuration of pieces after the collision is shown in the figure. The value of $\theta$ to the nearest integer is _________.

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Answer: 30

Before Collision

After Collision

From conservation of momentum along $x$ axis;
${\vec{P}}_{i}={\vec{P}}_{f}$
$10\times 10\sqrt{3}=200\cos \theta$
$\cos \theta =\dfrac{\sqrt{3}}{2}$
$\theta =30^{\circ}$