Question 82: Gravitation

Question

A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is :
(Given $$=$$ Radius of geo-stationary orbit for earth is $$4.2 	imes 10^4 \mathrm{~km}$$)

Accepted Answer

$$\begin{aligned}
& \frac{T_1}{T_2}=\left(\frac{r_1}{r_2}ight)^{3 / 2} \sqrt{\frac{m_2}{m_1}} \
& \Rightarrow \quad \frac{24}{6}=\left(\frac{4.2 	imes 10^4}{r_2}ight)^{3 / 2} \sqrt{\frac{m / 4}{m}} \
& \Rightarrow r_2=1.05 	imes 10^4 \mathrm{~km}
\end{aligned}$$

Answer

$$1.68 	imes 10^5 \mathrm{~km}$$

Answer

$$1.4 	imes 10^4 \mathrm{~km}$$

Answer

$$8.4 	imes 10^4 \mathrm{~km}$$

Answer

$$1.05 	imes 10^4 \mathrm{~km}$$

Gravitation

A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is : (Given $= Radius of geo-stationary orbit for earth is 4.2 \times 10^4 \mathrm{~km}$)

Choose the correct answer: