# A satellite moves in a circle around earth The radius of this circle is equal to one half of the radius of the moon's orbet. The satellite completes one revolution in

$a)\;\frac{1}{2}\; lunar month \\ b)\; \frac{2}{3} \;lunar\; month \\ c) 2^{\frac{3}{2}} lunar\; month\; \\ d)\; 2^{\large\frac{-3}{2}} \;lunar\; month$

Time period of revolution of moon around earth=1 lunar month
Time period $\alpha \; r^{\large\frac{3}{2}}$
$\Large\frac{T_s}{T_m}=\bigg(\frac{r_s}{r_m}\bigg)^{\Large\frac{3}{2}}=\bigg(\large\frac{1}{2}\bigg)^{\Large\frac{3}{2}}$
$T_s=2^{-\large\frac{3}{2}}$ lunar month
Hence d is the correct answer.

edited Feb 17, 2014 by meena.p