The ratio of energy required to raise a satellite of mass 'm' to a height ' h ' above the earth's surface to that required to put it into the orbit at same height is [ R = radius of the earth ]

Step-by-step solution

(D) Energy required to raise the satellite to a height h from surface of earth is given by aligned U &=- G M m (R+h) - (- G M m R ) &= G M m R - G M m (R+h) =G M m [ 1 R - 1 R+h ] &=G M m [ R+h-R R(R+h) ]=G M m h R(R+h) aligned KE of the satellite is given by aligned K &= 1 2 mV ₀²= 1 2 ~m GM ( R + h ) U K &= GMmh R ( R + h ) ( R + h ) 2 mGM = 2 ~h R aligned