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 rod of mass M and length L is made to stand vertically. Potential energy of the rod in this position 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 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-

A uniform rod of mass M and length L is hinged at its end. The rod is released from its vertical position by slightly pushing it. What is the reaction at the hinge when the rod becomes horizontal, again vertical.

A slender uniform rod of mass M and length l is pivoted at one ens so that it can rotate in a vertical plane, Fig. There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle theta with the vertical is