The arrangement shown in figure consists of two identical, uniform, solid cylinders, each of mass `m`, on which two light theads are wound symmetrically.
Find the tensions of each thread in the process of motion. The friction in the axle of the upper cylinder is assumed to be absent.

In the arrangement shown in figure the mass of the uniform solid cylindrical pulley of radius R is equal to m and the masses of two bodies are equal to m_(1) and m_(2) . The thread slipping and the friction in the axle of the pulley are supposed to be absent. Find the angular acceleration of the cylinder and the ratio of tensions (T_(1))/(T_(2)) of the vertical sections of the thread in the process of motion.

For the arrangement shown in the figure the coefficient of friction between the two blocks is mu . If both the blocks are identical and moving ,then the acceleration of each block is

A uniform cylinder of mass m rests on two rough horizontal planks. A thread is wound on the cylinder. The hanging end of the thread is pulled vertically down with a constant force F

A solid uniform cylinder of mass m performs small oscillations due to the action of two springs of stiffness k each (figure). Find the period of these oscillation in the absendce of sliding. x

A cylinder of mass m is suspended through two strings wrapped around it as shwon in figure . Find a. the tension T in the string and b. the speed o the cylinder as it falls through a distance h.

In the arrangement shown in figure, the string are light and intextensible. The surface over which blocks are placed is smooth. Find (a) the accelrations of the block (b) the tension in each string.

A uniform solid. cylinder A of mass can freely rotate about a horizontal axis fixed to a mount of mass m_(2) . A constant horizontal force F is applied to the end K of a light thread tightly wound on the cylinder. The friction between the mount and the supporting horizontal plane is assumed to be absent. Find the acceleration of the point K .

In the arrangement shown in figure two equal masses (each m) hung light cords wrapped around a uniform solid cylinder of mass M and radius R. The cylinder is free to roate about a harizontal axis. If the system is released from rest then, the tension in each cord is-

Two uniform cylinders, each of mass m = 10 kg and radius r = 150 mm, are connected by a rough belt as shown. If the system is released from rest, determine the tension in the portion of the belt connecting the two cylinders.