At what height from the surface of the earth, the total energy of satellite is equal to its potential energy at a height `2R` from the surface of the earth (`R`=radius of earth)

Options

A. `R/4`
B. `R/2`
C. 2R
D. 4R

Answer

B

Explanation

Total energy of a satellite at a height h = ` - (GMm)/(2(R + h))`
Potential energy at a height 2R from surface of earth
` = - (GMm)/((2R + R)) = - (GMm)/(3R)`
Given , ` - (GMm)/(2 (R + h)) = - (GMm)/(3R) " or " h = R/2`