Question

Three spheres each of mass $m$ are placed at the vertices of an equilateral triangle of side $l$. Each sphere is moving towards centroid with velocity $v$. After collision A comes to rest and B continues to move in the same direction with velocity $v$. Find the direction and magnitude of velocity of C after collision.

• A. C will move opposite to B with velocity $v$.
• B. C will come to rest.
• C. C will move in the direction of B with velocity $2v$.
• D. C will move in its original direction with velocity $v$.

Answer 1

The correct option is A C will move opposite to B with velocity $v$.

Let AB be X axis

Before collision:

Velocity of A = $vCos30°\hat{i}+vSin30°\hat{j}$

Velocity of B = $-vCos30°\hat{i}+vSin30°\hat{j}$

Velocity of C = $-v\hat{j}$

Net momentum of system before collision = m* ($vCos30°\hat{i}+vSin30°\hat{j}$) + m* ($-vCos30°\hat{i}+vSin30°\hat{j}$) + m * ($-v\hat{j}$) = 0

After collision:

Velocity of A = 0

Velocity of B= $-vCos30°\hat{i}+vSin30°\hat{j}$ = v

So for conservation of momentum, after collision too the net momentum = 0

=> m * velocity of B + m * velocity of C = 0

=> Velocity of C = - velocity of B

So C moves opposite to B with velocity v.