A block of mass `m` slides 0n a frictionless table. It is constrained to move inside a ring of radius `R` . At time `t=0` , block is moving along the inside of the ring (i.e. in the tangential direction) with velocity `v_(0)` . The coefficient of friction between the block and the ring is `mu` . Find the speed of the block at time `t` .

A semicircular ring of radius R is fixed on a smooth horizontal table. A small block is projected with speed u so as to enter the ring at end A. Initial velocity of the block is along tangent to the ring at A and it moves on the table remaining in contact with the inner wall of the ring. The coefficient of friction between the block and the ring is mu . (a) Find the time after which the block will exit the ring at B. (b) With what speed will the block leave the ring at B.

A block A of mass m_1 rests on a horizontal table . A light string connected to it passes over a frictionless pulley at the edge of table and from its other end another block B of mass m_2 is suspended . The coefficient of kinetic friction between the block and the table is mu . When the block A is sliding on the table the tension in the string is :

A block of mass m is moving on a rough horizontal surface. mu is the coefficient of kinetic friction between the block and the surface. What is the net force exerted by the surface on the block?

A block of mass m is pushed with a velocity v_(0) along the surface of a trolley car of mass M . If the horizontal ground is smooth and the coefficient of kinetic friction between the block of plank is mu . Find the minimum distance of relative sliding between the block and plank.

A block of mass m is pushed with a velocity v_(0) along the surface of a trolley car of mass M . If the horizontal ground is smooth and the coefficient of kinetic friction between the block of plank is mu . Find the minimum distance of relative sliding between the block and plank.

A block of mass m is projected up with a velocity v_0 along an inclined plane of angle of inclination theta=37^@ . The coefficient of friction between the inclined plane AB and blocks is mu(=tan theta) . Find the values of v_0 so that the block moves in a circular path from B to C.

A block of mass m_(2) is placed on a horizontal table and another block of mass m_(1) is placed on top is it. An increasing horizontal force F = alpha t is exerted on the upper block but the lowwer block never moves as a result. If the coefficient of friction between the blocks is mu_(1) coefficient of friction between the blocks is mu_(1) and that between the lower block and the table is mu_(2), then what is the maximum possible value of mu_(1)//mu_(2) ?

A block of mass m_(2) is placed on a horizontal table and another block of mass m_(1) is placed on top is it. An increasing horizontal force F = alpha t is exerted on the upper block but the lowwer block never moves as a result. If the coefficient of friction between the blocks is mu_(1) coefficient of friction between the blocks is mu_(1) and that between the lower block and the table is mu_(2), then what is the maximum possible value of mu_(1)//mu_(2) ?