A light elastic string whose natural length is a has one end fixed point O, and to the other end is attached a weight which in equilibrium would produce an extension e. Show that it the weight be let fall from rest at O, it will come to stay instantaneously at a point √(2ae + e2 ) below the position of equilibrium.

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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