A square plate of moment of inertia `I` is pivoted at its centre. It has a small projection of negligible mass to one of its sides. A particle of mass m moving with a velocity v parallel to the side having projection strikes to projection and stricks to it. If `l` is the side length, the angular velocity of plate is

A uniform rod of mass M and length L lies on a frictionless horizontal plane. A particle of same mass M moving with speed v_(0) perpendicular to the length of the rod strikes the end of the rod and sticks to it. Find the velocity of the center of mass and the angular velocity about the center of mass of (rod + particle) system.

A thin uniform square plate with side l and mass M can rotate freely about a stationary vertical axis coinciding with one of its sides. A small ball of mass m flying with velocity v at right angles to the plate strikes elastically the centre of it. Find: (a) the velocity of the ball v^' after the impact, (b) the horizontal component of the resultant force which the axis will exert on the plate after the impact.

A square plate has a moment of inertia l_(0) about an axis lying in its plane, passing through its centre and making an angle theta with one of the sides. Which graph represents the variation of l with theta ?

A particle of mass m is projected with velocity v at an angle theta with the horizontal. Find its angular momentum about the point of projection when it is at the highest point of its trajectory.

A thin uniform square plate with side l and mass M can rotate freely abouta stationary vertical axis coinciding with one of its sides . A small ball of mass m flying with velocity v at right angles to the plate strikes elastically to the centre of it. Find the velocity of the ball v'after the impact and the horizontal component of the force which the axis will exert on the plate after the impact. [(3m-4M)/(3m+ 4M)v , (72Mm^(2)v^(2))/(l(3m+ 4m)^(2))]

A particle of mass m is projected with a velocity mu at an angle of theta with horizontal.The angular momentum of the particle about the highest point of its trajectory is equal to :

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 kept on a frictionless horizontal floor. A particle of mass m moving perpendicular to the rod with a speed v strikes at the end of the rod and sticks there. Calculate angular velocity acquired by the combined system.

A uniform rod of length L lies on a smooth horizontal table. The rod has a mass M . A particle of mass m moving with speed v strikes the rod perpendicularly at one of the ends of the rod sticks to it after collision. Find the velocity of the centre of mass C and the angular, velocity of the system about the centre of mass after the collision.