Question

A ball of mass 10 kg moving with a velocity 10√3 m/s along the x-axis, hits another ball of mass 20 kg 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 y-axis with a speed of 10 m/s. The second piece starts moving at an angle of 30° with respect to the x-axis. The velocity of the ball moving at 30° with x-axis is x m/s. The value of x to the nearest integer is __________. 

Hint:

In 2D collisions, solve momentum equations independently for the x and y directions.

Answer 1

Correct Answer: 20

Step 1: Apply Conservation of Linear Momentum. Initial Momentum $\vec{P_i} = (10 \times 10\sqrt{3})\hat{i} = 100\sqrt{3}\hat{i}$.
Step 2: Disintegrated pieces of 20 kg are two 10 kg masses. $\vec{P_f} = (10 \times 10)\hat{j} + (10 \times v \cos 30^\circ)\hat{i} - (10 \times v \sin 30^\circ)\hat{j}$.
Step 3: X-axis: $100\sqrt{3} = 10 v (\sqrt{3}/2) \implies v = 20 \text{ m/s}$.
Step 4: Y-axis check: $100 - 10 v(1/2) = 100 - 10(10) = 0$. (Conserved). The velocity $x = 20$.