A body is projected vertically upwards from the surface of the Earth with an initial velocity exactly equal to the orbital velocity of a satellite revolving very close to the Earth's surface. The maximum height reached by the body is ( R is the radius of the Earth):

Step-by-step solution

The orbital velocity of a satellite revolving very close to the Earth's surface is given by v_o = GM R . Let the maximum height reached by the body be h . Applying the principle of conservation of mechanical energy between the surface of the Earth and the maximum height: 1 2 mv_o^2 - GMm R = - GMm R+h Substituting v_o^2 = GM R : 1 2 m ( GM R ) - GMm R = - GMm R+h - GMm 2R = - GMm R+h R+h = 2R h = R Using the constant gravity approximation ( mgh = 1 2 mv^2 ) incorrectly yields h = R 2 , and forgetting to subtract R