Consider a rod of mass `M` and length `L` pivoted at its centre is free to rotate in a vertical position plane. The rod is at rest in the vertical position. A bullet of mass `M` moving horizontally at a speed `v` strikes and embedded in one end of the rod. The angular velocity of the rod just after the collision will be.

Moment of inertia of uniform rod of mass M and length L about an axis through its centre and perpendicular to its length is given by (ML^(2))/(12) . Now consider one such rod pivoted at its centre, free to rotate in a vertical plane. The rod is at rest in the vertical position. A bullet of mass M moving horizontally at a speed v strikes and embedded in one end of the rod. The angular velocity of the rod just after the collision will be

A rod of mass m,length l pivoted at its centre is free to rotate in a vertical plane.The rod is at rest and is in vertical position.A bullet of mass m/2 moving horizontally with speed v strikes and sticks to one end of the rod. Angular velocity of system just after collision is

A uniform rod of mass m and length L is at rest on a smooth horizontal surface. A ball of mass m, moving with velocity v_0 , hits the rod perpendicularly at its one end and sticks to it. The angular velocity of rod after collision is

A rod of length l is released from the vertical position on a smooth horizontal plane. What is the nature of motion of the free end of the rod ?

A homogenous rod XY of length L and mass 'M' is pivoted at the centre 'C' such that it can rotate freely in vertical plane. Initially the rod is in the horizontal position.

A uniform rod of mass m and length / is hinged at upper end. Rod is free to rotate in vertical plane. A bail of mass m moving horizontally with velocity vo collides at lower end of rod perpendicular to it and sticks to it. The minimum velocity of the ball such that combined system just completes the vertical circle will be

A rod of mass 4m and length L is hinged at the mid point. A ball of mass 'm' moving with speed V in the plane of rod, strikes at the end at an angle of 45^@ and sticks to it. The angular velocity of system after collision is-