The ratio of the energy required to raise a satellite upto a height h above the earth of radius R to that the kinetic energy of the satellite into that orbit is

Options

A. `h : 2R`
B. `2h : R`
C. `R:h`
D. `h:R`

Answer

B

Explanation

`E_(1)=DeltaU=((mgh)/(1+h//R))`
`E_(2)=` Energy of satellite-energy of satellite on surface of earth
`=-(GMm)/(2(R+h))+(GMm)/(R)=mgR[1-(1)/(2(1+h//R))]`
`rArr E_(2)=(mgR((2h)/(R)+1))/(2(1+(h)/(R)))`
`:. (E_(1))/(E_(2))=(mgh)/(1+(h)/(R))xx(2(1+(h)/(R)))/(mgR)=(2h)/(R)" "((because h lt ltR),( :. 1 + (2h)/(R)~~ 1))`.