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

Answer: (D)

$t=k{{\rho }^{-1/2}}$

Answer 2

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