A cockroach, mass m, runs counterclockwise around the rim of a lazy Susan (a circular dish mounted on a vertical axle) of radius R and rotational inertia I with frictionless bearings. The cockroach's speed (relative to the Earth) is v, whereas the lazy Susan turns clockwise with angular speed ω. The cockroach finds a bread crumb on the rim and, of course, stops. Find the angular speed of the lazy Susan after the cockroach stops.

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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