Consider two objects of different masses connected by a cable passing over a massless and frictionless Pulley. Derive expressions for the tension in the cable and acceleration of the objects.

Two blocks of masses 2kg and 5kg are at rest on ground. The masses are connected by a string passing over a frictionless pulley which is under the influence of a constant upward force F = 50 N. Find the accelerations of 5kg and 2kg masses.

A block of mass 3 kg which is on a smooth inclined plane making an angle of 30° to the horizontal is connected by a cord passing over a light frictionless pulley to a second block of mass 2 kg hanging vertically. What is the acceleration of each block and what is the tension of the cord?

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.