A rope of mass M uniformly distributed along its length L, can slode without friction on a horizontal table. At instant t=0 the hanging part of the rope has a length b, and the rope is held at rest. When it is left, the rope begins to slide. At instant t the part of the rope that hangs has a length x and velocity v. The horizontal table is the reference level of gravitational potential energy. Calculate the mechanical energy of the system in terms of M, L, x, v, and g. Thank you.

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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