Two identical satellites are moving around the earth in circular orbits at heights 3R and R respectively where R is the radius of the Earth. The ratio of their kinetic energies is

Question

Two identical satellites are moving around the earth in circular orbits at heights 3R and R respectively where R is the radius of the Earth. The ratio of their kinetic energies is (A) 2:1 (B) 1:2 (C) 3:1 (D) 2:3

Tardigrade Admin · Accepted Answer

The kinetic energy of satellites in a circular orbit is given as Ek=(G M m/2 r)⇒ (Ek1/Ek2)=(r2/r1)=(R + R/R + 3 R)=(2 R/4 R)=(1/2)

Q. Two identical satellites are moving around the earth in circular orbits at heights $3 R$ and $R$ respectively where $R$ is the radius of the Earth. The ratio of their kinetic energies is

$2 : 1$

$1 : 2$

$3 : 1$

$2 : 3$

The kinetic energy of satellites in a circular orbit is given as
$E_{k} = \frac{GM m}{2 r} \Rightarrow \frac{E _{k_{1}}}{E _{k_{2}}} = \frac{r _{2}}{r _{1}} = \frac{R + R}{R + 3 R} = \frac{2 R}{4 R} = \frac{1}{2}$

Q. Two identical satellites are moving around the earth in circular orbits at heights 3R and R respectively where R is the radius of the Earth. The ratio of their kinetic energies is

2:1

1:2

3:1

2:3