A hollow vertical cylinder of radius R and height h has smooth internal surface. A small particle is placed in contact with the inner side of the upper rim at a point P. It is given a horizontal speed `V_0` tangential to rim. It leaves the lower rim at point Q, vertically below P. The number of revolutions made by the particle will be:

A hollow vertical cylinder of radius R and height h has a smooth internal surface. A small particle is held in contact with the inner side of upper rim at a point P. It is given a horizontal speed v_(0) tangential to rim. It leaves the lower rim at point Q, vertically below P. The number of revolutions made by the particle will be [Take acceleration due to gravity g]

A hollow vertical cylinder of radius r and height h has a smooth internal surface. A small particle is placed in contact with the inner side of the upper rim, at point A, and given a horizontal speed u, tangentical t the rim. it leaves the lower rim at point B, vertically below A. If n is an integer then

In figure, a particle is placed at the highest point A of a smooth sphere of radius r. It is given slight push, and it leaves the sphere at B, at a depth h vertically below A. The value of h is

A small particle is placed at the top point A of a fixed smooth hemisphere of radius R. Particle is given small displacement towards right and it starts slipping. Calculate velocity of the particle after hitting horizontal perfectly inelastic surface.

A cylinder of radius R = 1 m and height H = 3 m two- thirds filled with water, is rotated about its vertical axis as shown in Fig. Determine the speed of rotation when a. the: water just starts spilling over the rim. b. the point at the centre of the base is just exposed.

A particle of mass m moves along the internal smooth surface of a vertical cylinder of the radius R. Find the force with which the particle acts on the cylinder wall if at the initial moment of time its velocity equals v_(0) . And forms an angle alpha with the horizontal.

A horizontal plane supports a fixed vertical cylinder of radius R and a particle is attached to the cylinder by a horizontal thread AB as shown in Fig. The particle initially rest on a horizontal plane. A horizontal velocity v_(0) is imparted to the particle, normal to the threading during subsequent motion. Point out the false statements:

A small particle of mass m is fixed to the perimeter of a ring of same mass and radius r. The system comprising of particle and ring is placed on a horizontal plane. Friction is negligible on horizontal plane. Initially particle is at top most point, then the system is released from rest. Answer next two question when the particle is at the same height as the centre of ring aftr being released from top most point. Assume that the ring stays in vertical plane during its motion under consideration Mark the CORRECT option(s):

A uniform circular ring of mass m and radius R is placed freely on a horizontal smooth surface as shown in figure. A particle of mass m is connected to the circumference of the ring with massless string . The particle is imparted velocity v_0 perpendicular to length of string as shown. If T is tension in the string just after the particle imparted velocity , then Acceleration of point P at this instant , is

A horizontal cylinder is fixed, its inner surface is smooth and its radius is R. A small block is initially at the lowest point. The minimum velocity that should by given to the block at the lowest point, so that it can just cross the point P is u then