Three identical balls are connected by light inextensible strings with each other as shown and placed over a smooth horizontal table. Length of each string is l . At moment t = 0 , ball B is imparted a velocity v 0 perpendicular to the string and then the system is left on its own. The speed of A at the instant just before it collides with C is

Question

Three identical balls are connected by light inextensible strings with each other as shown and placed over a smooth horizontal table. Length of each string is l . At moment t = 0 , ball B is imparted a velocity v 0 perpendicular to the string and then the system is left on its own. The speed of A at the instant just before it collides with C is, v 0 3, 2 v 0 3, 2 v 0 5, 2 v 0 9

MARKS App · Accepted Answer

Using conservation of linear momentum along the initial direction of motion of B we get, m v 0 = 3 m v v = v 0 3 The total kinetic energy of the system will remain the same 1 2 m v 0 2 = 1 2 m v 2 + 2 1 2 m v 2 + v 1 2 where v 1 is the component of velocity of A and C perpendicular to the initial direction of motion of B v 0 2 = v 0 3 2 + 2 v 0 3 2 + 2 v 1 2 v 1 2 = v 0 2 3 Velocity of A = v 2 + v 1 2 = 2 3 v 0

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