A GUN IS MOUNTED ON A MOVABLE GUN CARRIAGE WHICH IS ON A SMOOTH HORIZONTAL PLANE. THE GUN IS ELEVATED AT AN ANGLE a TO THE HORIZONTAL. A SHOT IS FIRED AND LEAVES THE GUN IN A DIRECTION INCLINED AT AN ANGLE b TO THE HORIZONTAL. IF THE MASS OF THE GUN AND THE CARRIAGE IS n TIMES THE MASS OF THE SHOT, THEN SHOW THAT:

tan b=(1 + 1/n) tan a

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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