Question

Time period of revolution is T for any satellite revolving around a planet of radius R. The period of revolution for the satellite around another planet having the same density($\rho$) radius as 3R, is__. (Assume the satellite to be very near to the planet's surface)

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

Answer 1

The correct option is B T

Time period of satellite which is very near to planet
$T=2\pi \sqrt{\frac{R^3}{GM}}=2\pi \sqrt{\frac{R^3}{G\frac{4}{3}\pi R^3\rho }}$
$\therefore T\propto \sqrt{\frac{1}{\rho }}$
i.e. time period (T) of nearest satellite does not depends upon the radius of planet, it only depends upon the density of the planet. In the problem, density is same so time period will be same.