The Earth was formed about 4.5 billion years ago, probably as a sphere of roughly uniform density. Shortly thereafter, heat from the decay of radioactive elements caused much of the Earth to melt. This allowed the heavier material to sink to- ward the center of the Earth, forming the core. Today, we can picture the Earth as made up of a core of radius 3570 km and density 10.3 g/cm³ surrounded by a mantle of density 4.50 g/cm³ extending to the surface of the Earth (radius 6370 km). We ignore the crust of the Earth. Calculate the fractional change in the length of the day due to the formation of the core.

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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