- Home
- Standard 11
- Physics
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 statement is true ?
The potential energies of earth and satellite system in the two cases are equal.
$S_1$ and $S_2$ are moving with the same speed.
The kinetic energies of the two satellites are equal.
The time period of $S_1$ is four times that of $S_2$.
Solution
Orbital velocity $\mathrm{V}_{0}=\sqrt{\frac{\mathrm{GM}}{\mathrm{r}}}$
$\mathrm{P.E.}=\frac{-\mathrm{GM}_{\mathrm{e}} \mathrm{m}_{\mathrm{s}}}{\mathrm{r}} \quad \therefore$ masses are different
$\Rightarrow \mathrm{P.E.}$ are different
$\mathrm{KE}=\frac{1}{2} \mathrm{mv}^{2}$
$\mathrm{T}^{2} \propto \mathrm{r}^{3} \Rightarrow \mathrm{T}_{1}=\mathrm{T}_{2}$
