A launching vehicle carrying an artificial satellite of mass m is set for launch on the surface of the earth of mass M and radius R . If the satellite is intended to move in a circular orbit of radius 7R , the minimum energy . Required to be spent by the launching vehicle on the required to be spent by the launching vehicle on the satellite is (Gravitational constant =G)

Options

A. `GMm/R`
B. `- 13GMm/14R`
C. `GMm/7R `
D. `GMm/14R`

Answer

B

Explanation

The energy of an artificial satellite at the surface of the earth is given by , E, =`(GMm)/R`
If the satellite is intended to move in a circular orbit of radius 7R then, the energy of satellite becomes,
E_2= `((-1)/2) (GMm)/7R`
The minimum energy required is
`E= E_1-E_2`
=`( (-GMm)/(R))+ 1/2 (GMm)/7R`
= `(-14 GMm+ GMm)/14R`
`therefore E = (-13GMm)/14R`