Question

Two satellites of earth $S_1$ and $S_2$ are moving in the same orbit. The mass of $S_1$ is four times the mass of $S_2$. Which one of the following statements is true?

• A. The potential energies of earth and satellite in the two cases are equal.
• B. $S_1$ and $S_2$ are moving with the same speed.
• C. The kinetic energies of the two satellites are equal.
• D. The time period of $S_1$ is four times that $S_2$.

Answer 1

Answer: (B)

$S_1$ and $S_2$ are moving with the same speed.

Both orbital speed of satellite $v_o=\sqrt{\frac{G{M}_E}{r}}$ and time period of revolution of satellite, $T={\left[\frac{4{\pi }^2{r}^3}{G{M}_E}\right]}^{1/2}$ are independent of mass of satellite. Therefore orbital speed and time period of revolution of bot the satellites are same. Hence, option (b) is correct.

The kinetic energy of a satellite, $K=\frac{G{M}_{E}m}{2r}$

and potential energy of a satellite, $U=\frac{G{M}_{E}m}{r}$

Both depend on the mass of the satellite, vary with mass of the satellite.