Two objects, each of mass m, hang from strings of different lengths on a balance at the surface of the Earth, as shown. If the strings have negligible mass and differ in length by h, (a) show that the error in weighing, associated with the fact that W’ is closer to the Earth than W, is W’ – W = 8piGpmh/3, where p is the mean density of the Earth (5.5 g/cm^3). (b) Find the difference in length that will give an error of one part in a million.

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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