A cylinder of mass M and radius R lies on a plank of mass M as shown. The surface between plank and ground is smooth, and between cylinder and plank is rough. Assuming no slipping between cylinder and plank, the time period of oscillation (When displaced from equilibrium) of the system is

A cylinder of mass M = 2 kg and radius R = 12 cm lies on a plank of the same mass as shown in the figure. The surface between plank and ground is smooth but there is friction between cylinder and plank. If the coefficient of friction between the cylinder and the plank is mu=0.4 , then what maximum initial compression (in cm) can be given to the spring such that the cylinder moves without slipping with respect to the plank ? ["Given, "k="200 N m"^(-1)]

A solid sphere of mass m and radius R is placed over a plank of same mass m . There is sufficient friction between sphere and plank to prevent slipping. Force of friction between sphere and plank is

A solid sphere of mass m and radius R is placed over a plank of same mass m . There is sufficient friction between sphere and plank to prevent slipping. Force of friction between sphere and plank is

A uniform plank of mass m, free to move in the horizontal direction only , is placed at the top of a solid cylinder of mass 2 m and radius R. The plank is attached to a fixed wall by mean of a light spring constant k. There is no slipping between the cylinder and the planck , and between the cylinder and the ground. Find the time period of small oscillation of the system.

A uniform plank of mass m, free to move in the horizontal direction only , is placed at the top of a solid cylinder of mass 2 m and radius R. The plank is attached to a fixed wall by mean of a light spring constant k. There is no slipping between the cylinder and the planck , and between the cylinder and the ground. Find the time period of small oscillation of the system.

A cylinder of radius R is to roll without slipping between two planks as shown in the figure. Then

A solid sphere of mass m and radius R is placed over a plank of same mass m . There is sufficient friction between sphere and plank to prevent slipping. Acceleration of centre of mass of sphere is