A particle having velocity V = _V0 at t = 0 is decelerated at the rate |a| = β √V , where β is a positive constant. Choose the correct option(s) :-

(a) The particle comes to rest at t = (2 √_{V0 ) /} β

(b) The particle will come to rest at infinty

(c) The distance travelled by the particle is (2 _{V0 ^3/2 ) /} β

(d) The distance travelled by the particle is (2 _{V0 ^3/2 ) /} 3β

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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