A pulley having a rotational inertia of 1.14×10^–3kg.m^2 and a radius of 9.88 cm is acted on by a force , applied tangentially at its rim , that varies in time as=0.496t + 0.305t^2 where F is in Newton`s and t is in second .If the pulley was initially at rest, find its angular speed after 3.60s.

Three identical balls are placed on a frictionless horizontal surface touching each other. They stick to each other because of adhesive. Another ball of same radius and mass m is placed over the void created by the three balls. Find the forces applied by the balls kept on the floor to each other if the system remains in equilibrium.

A car loaded with water having total mass 1000 kg moves on a straight horizontal Road starting from rest under the action of a force of 100 Newton. The water spills throw a small hole in the bottom at a rate of 0.1 KG per second the velocity of cart after 300 seconds is nearly.

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