Question

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 the earth$)$

• A. $2R$
• B. $\frac{R}{2}$
• C. $\frac{R}{4}$
• D. $4R$

Answer 1

The correct option is B $\frac{R}{2}$

Total Energy at an height $H=\frac{-6Mm}{2[h+R]}$

$\therefore$ Potential Energy at height $2R=\frac{-6Mn}{(2R+R)}$

$\frac{-6Mm}{+2[h+R]}=\frac{-6Mm}{[2R+R]}$

$\therefore \frac{1}{2h+2R}=\frac{1}{3R1}$

$3R=2h+2R$

$R=2H$

$H=\frac{R}{2}$