Question

Time period of a satellite in an orbit of radius R is T. Its period of revolution in an orbit of radius 4R will be

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

Answer 1

The correct option is B $2\sqrt{2}T$

Since time period depends upon radius of orbit as $T^2\propto R^3$ or $T\propto R^{\frac{3}{2}}$

Hence for orbit of radius $4R$ the time period is:

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

$\Rightarrow T^{\prime }=2\sqrt{2}T$