Question

Satellite revolve in radius $R$ has a time period of revolution $T$. Find time period of a satellite if orbital radius is $9R$ ?

• A. $3\sqrt{3}T$
• B. 9T
• C. 27 T
• D. $9\sqrt{3}T$

Answer 1

Answer: (C)

According to Kepler's law of periods
$T^{2}\,\propto\,R^{3}$
So,$\,\Rightarrow \, \frac{T_{1}}{T_{2}}=\left(\frac{R_{1}}{R_{2}}\right)^{\frac{3}{2}}$
$\Rightarrow \, \frac{T}{T_{2}}=\left(\frac{R}{9R}\right)^{\frac{3}{2}}\,=\frac{1}{27}\,\left[\because \,T_{1}=T\right]$
$T_{2}=27T$