A uniform rod of mass m and length 2L on a smooth horizontal surface. A particle of mass m is connected to a string of length L whose other end is connected to the end ‘A’ of the rod. Initially the string is held taut perpendicular to the rod and the particle is given a velocity `v_(0)` parallel to the initial position of the rod. (a) Calculate the acceleration of the centre of the rod immediately after the particle is projected. (b) The particle strikes the centre of the rod and sticks to it. Calculate the angular speed of the rod after this.

A uniform rod of mass m and length 2L on a smooth horizontal surface.

1.	A uniform rod of mass m and length 2L on a smooth horizontal surface. A particle of mass m is connected to a string of length L whose other end is connected to the end ‘A’ of the rod. Initially the string is held taut perpendicular to the rod and the particle is given a velocity `v_(0)` parallel to the initial position of the rod. (a) Calculate the acceleration of the centre of the rod immediately after the particle is projected. (b) The particle strikes the centre of the rod and sticks to it. Calculate the angular speed of the rod after this.
Answer» Correct Answer - (a) `(v_(0)^(2))/(5L)` (b) `(3)/(2) (v_(0))/(L)`

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