The engine of a train passes an electric pole with a velocity ’$u$’ and the last compartment of the train crosses the same pole with a velocity $v$. Then find the velocity with which the mid-point of the train passes the pole. Assume acceleration to be uniform.

Calculate the acceleration of the system, tension in the string and thrust on the pulley in terms of g for the situation shown in following diagram.

Two blocks of masses 8kg and 4 kg respectively are connected by a string as shown. Calculate their accelerations if they are initially at rest on the floor, after a force of 100N is applied on the pulley in the upward direction (g = 10 m/s²)