A body of mass ' m ' is raised vertically from the surface of the Earth. If the work done against gravity is 3 4 mgR , where ' g ' is the acceleration due to gravity at the surface and ' R ' is the radius of the Earth, the height attained by the body is :

Step-by-step solution

The work done against gravity in raising a mass m to a height h from the Earth's surface is given by the change in gravitational potential energy. Initial potential energy, U_i = - GMm R Final potential energy, U_f = - GMm R+h Work done, W = U_f - U_i = GMm R - GMm R+h = GMmh R(R+h) Using GM = gR^2 , we get: W = mgh 1 + h R Given that W = 3 4 mgR , we equate the two expressions: mgh 1 + h R = 3 4 mgR h 1 + h R = 3 4 R 4h = 3R (1 + h R ) 4h = 3R + 3h h = 3R Answer: 3R