Question

A artificial satellite is going round the earth assumed to be uniform sphere. Its period t will depend on the density $ \rho $ by the relation (k is numerical constant)

• A. $ t=k{{\rho }^{1/2}} $
• B. $ t=k\rho $
• C. $ t=k{{\rho }^{-1}} $
• D. $ t=k{{\rho }^{-1/2}} $

Answer 1

The Correct Option is D

Time period of satellite is given by $ t=2\pi \sqrt{\frac{{{R}^{3}}}{GM}}=2\pi \sqrt{\frac{{{R}^{3}}}{G\left( \frac{4}{3} \right)\pi {{R}^{3}}\rho }} $ $ \Rightarrow $ $ t\propto \frac{1}{\sqrt{\rho }} $