A rod of uniform cross-section of mass M and length L is hinged about an end to swing freely in a vertical plane.However,its density is non-uniform and varies linearly from hinged end to the free end doubling its value. The moment of inertia of the rod,about the rotation axis passing through the hinge point is

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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