Under what conditions could unequal masses by strung over a pulley without the pulley having any tendency to turn ?

A man with mass 85 kg stands on a platform with mass 25 kg. He pulls on the free end of a rope that runs over a pulley on the ceiling and has its other end fastened to the platform. The mass of the rope and the mass of the pulley can be neglected, and the pulley is frictionless. With what force does he have to pull so that he and the platform have an upward acceleration of 2.2m/s^(2) . (Take g= 10m/s^(2) )

A uniform chain of mass m hangs from a light pulley, with unequal lengths of the chain hanging from the two sides of the pulley. The force exerted by the moving chain on the pulley is

Two men of unequal masses hold on to the two sections of a light rope passing over a smooth light pulley. Which of the following are possible ?

Two men of unequal hold to the two sections of a light rope passing over a smooth light pulley. Which of the following are possible ?

In figure mass m_(1) slides without friction on the horizontal surface, the frictionless pulley is in the form of a cylinder of mass M and radius R , and a string turns the pulley without slipping. Find the acceleration of each mass, and tension in each part of the string.

A block of mass m is attached at the end of an inextensible string which is wound over a rough pulley of mass M and radius R figure a. Assume the stirng does not slide over the pulley. Find the acceleration of the block when released.

A rope thrown over a pulley has a ladder with a man of mass m on one of its ends and a counter balancing mass M on its other end. The man climbs with a velocity v_r relative to ladder. Ignoring the masses of the pulley and the rope as well as the friction on the pulley axis, the velocity of the centre of mass of this system is: