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

Two unequal masses are connected by a very light string over a clamped light smooth pulley. Find the acceleration of the system and the tension in the string.

Two unequal masses are connected by a very light string over a clamped light smooth pulley. Find the acceleration of the system and the tension in the string.

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.