Center of Mass, Momentum & Collision

JEE Main level, numerical answer, medium

100 of 130

Question 100 of 130

A ball of mass 10kg10kg moving with a velocity 103ms−110\sqrt{3}m{s}^{-1} along the xx -axis, hits another ball of mass 20kg20kg which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along yy -axis with a speed of 10ms−1.10m{s}^{-1}. The second piece starts moving at an angle of 30∘30^{\circ} with respect to the xx -axis. The velocity of the ball moving at 30∘30^{\circ} with xx -axis is xms−1.xm{s}^{-1}. The configuration of pieces after the collision is shown in the figure below. The value of xx to the nearest integer is

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Answer: 20

Let the velocity of 2nd{2}^{\text{nd}} fragment is v⃗\vec{v} then by conservation of linear momentum
10(103)i^=(10)(10j^)+10v⃗10(10\sqrt{3})\hat{i}=(10)(10\hat{j})+10\vec{v}
⇒v⃗=103i^−10j^\Rightarrow \vec{v}=10\sqrt{3}\hat{i}-10\hat{j}
∣v⃗∣=300+100=400=20ms−1|\vec{v}|=\sqrt{300+100}=\sqrt{400}=20m{s}^{-1}.

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