In the figure, the disc `D` does not slip on the surface `S`, the pulley `P` has mass and the string does not slip on it. The string is wound around the disc.

In the fig the pulled has a mass M , radius r and the string does not slip over it. The time period of oscillation is

Solve the previous problem if the pulley has a moment of inertia I about its axis and the string does not slip over it.

A uniform solid cylinder of mass m and radius 2R rests on a horizontal table. A string attached to it passes over a pulley (disc) of mass m and radius R that is mounted on a fricitonaless axle through its centre . A block of mass m is suspended from the free end of the spring . The string does not slip over the pulley surface and the cylinder rolls without slipping on the table. Acceleration of the block is

A uniform solid cylinder of mass m and radius 2R rests on a horizontal table. A string attached to it passes over a pulley (disc) of mass m and radius R that is mounted on a fricitonaless axle through its centre . A block of mass m is suspended from the free end of the spring . The string does not slip over the pulley surface and the cylinder rolls without slipping on the table. Angular acceleration of the cylinder is

A uniform solid cylinder of mass m and radius 2R rests on a horizontal table. A string attached to it passes over a pulley (disc) of mass m and radius R that is mounted on a fricitonaless axle through its centre . A block of mass m is suspended from the free end of the spring . The string does not slip over the pulley surface and the cylinder rolls without slipping on the table. Angular acceleration of the cylinder is

A uniform solid cylinder of mass m and radius 2R rests on a horizontal table. A string attached to it passes over a pulley (disc) of mass m and radius R that is mounted on a fricitonaless axle through its centre . A block of mass m is suspended from the free end of the spring . The string does not slip over the pulley surface and the cylinder rolls without slipping on the table. Force of friction acting on the cylinder is

A uniform solid cylinder of mass m and radius 2R rests on a horizontal table. A string attached to it passes over a pulley (disc) of mass m and radius R that is mounted on a fricitonaless axle through its centre . A block of mass m is suspended from the free end of the spring . The string does not slip over the pulley surface and the cylinder rolls without slipping on the table. Force of friction acting on the cylinder is

A uniform solid cylinder of mass m and radius 2R rests on a horizontal table. A string attached to it passes over a pulley (disc) of mass m and radius R that is mounted on a fricitonaless axle through its centre . A block of mass m is suspended from the free end of the spring . The string does not slip over the pulley surface and the cylinder rolls without slipping on the table. Acceleration of the block is