A uniform rod AB of length L and mass M is lying on a smooth table. A small particle of mass m strikes the rod with velocity V 0 at point C at a distance x from the centre O . The particle comes to rest after collision. If the value of x , so that the point A of the rod remains stationary just after the collision, is L / n , then find n .

Question

A uniform rod AB of length L and mass M is lying on a smooth table. A small particle of mass m strikes the rod with velocity V 0 at point C at a distance x from the centre O . The particle comes to rest after collision. If the value of x , so that the point A of the rod remains stationary just after the collision, is L / n , then find n ., 6, 4, 12, 8

MARKS App · Accepted Answer

mv o = MV cm ⇒ V cm = mv o /M mv o x = 1 12 M L 2 ω ⇒ ω = 12 m v o x M L 2 V A G = 0 ⇒ V A C + V C G = 0 ⇒ - ω L 2 + m v o M = 0 ⇒ m v o M = 12 m v o x M L 2 × L 2 ⇒ x = L/6

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