(a) Show that the sum of the rotational inertias of a plane laminar body about any two perpendicular axes in the plane of the body is equal to the rotational inertia of the body about an axis through their point of intersection perpendicular to the plane. (b) Apply this to a circular disk to find its rotational inertia about a diameter as axis.

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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