Question

The time period of a satellite in an orbit of radius $R$ is $T$. The time period of another identical satellite in an orbit of radius $4R$ will be

• A. $4T$
• B. $2T$
• C. $2\sqrt{2}T$
• D. $8T$

Answer 1

The correct option is D $8T$

We have $T^2\propto R^3$

$\frac{T_1}{T_2}={\left(\frac{R_1}{R_2}\right)}^{\left(3/2\right)}$

$={\left(\frac{R}{4R}\right)}^{\left(3/2\right)}$

$⟹T_{\left(2\right)}=8T_{\left(1\right)}$