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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.
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B
C will come to rest.
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C
C will move in the direction of B with velocity 2v.
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D
C will move in its original direction with velocity v.
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Solution

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°^i+vSin30°^j
Velocity of B = vCos30°^i+vSin30°^j
Velocity of C = v^j
Net momentum of system before collision = m* (vCos30°^i+vSin30°^j) + m* (vCos30°^i+vSin30°^j) + m * (v^j) = 0

After collision:
Velocity of A = 0
Velocity of B= vCos30°^i+vSin30°^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.

396922_138189_ans.jpg

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