Question

At a height $H$ from the surface of the earth, the total energy of a satellite is equal to the potential energy of a body of equal mass at a height of $3R$ from the surface of earth ($R=$ Radius of the earth). The value of $H$ is:

• A. $R$
• B. $\frac{4R}{3}$
• C. $3R$
• D. $\frac{R}{3}$

Answer 1

The correct option is A $R$

Total energy of the body $T.E=\frac{-GMm}{2r}$ where $r$ is the distance of body from center of earth

$\therefore$ $r=R+H$

$⟹$ $T.E=\frac{-GMm}{2(R+H)}$ ...........(1)

Potential energy $P.E=\frac{-GMm}{(R+3R)}=\frac{-GMm}{4R}$ ...........(2)

According to the question, $\frac{-GMm}{2(R+H)}=\frac{-GMm}{4R}$

or, $R+H=2R$

or, $H=R$