A straight, smooth tunnel is dug through a uniform spherical planet of mass density ? P. The tunnel passes through the center of the planet and is perpendicular to the planet''s axis of rotation, which is fixed in space. The planet rotates with a constant angular speed w so that objects in the tunnel have no apparent weight. Find the required angular speed of the planet ?.

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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