A body starts from rest at a point, distance R 0 from the centre of the earth of mass M , radius R . The velocity acquired by the body when it reaches the surface of the earth will be

Question

A body starts from rest at a point, distance R 0 ​ from the centre of the earth of mass M , radius R . The velocity acquired by the body when it reaches the surface of the earth will be

TestHub · Accepted Answer

Initial total energy = Initial kinetic energy + initial potential energy = 2 1 ​ m ( 0 ) 2 + ( − R 0 ​ GM m ​ ) = − R 0 ​ GM m ​ Total energy, when it reaches the surface of earth = 2 1 ​ m v 2 + ( − R GM m ​ ) Applying energy conservation, ​ 2 1 ​ m v 2 − R GM m ​ = − R 0 ​ GM m ​ ​ v = 2 GM { R 1 ​ − R 0 ​ 1 ​ } ​ Ans. ​

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