A semi-cylindrical groove of radius r = 30 cm is made on a horizontal floor. An ant wants to cross the groove. A boy decides to help the ant by making a bridge consisting of two straight wire segments. The length of each wire available is 51 cm. So the boy connects two wires at right angle and place the bridge in the groove as shown in figure. If the ant can crawl up any wire segment at speed v = 1 cm/s and down any wire segment at speed 3v, then minimum time in which ant can cross the groove is

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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