Q. A satellite is revolving round the earth in an orbit of radius $r$ with time period $T$. If the satellite is revolving round the earth in an orbit of radius $r + \Delta r(\Delta r \ll r)$ with time period $T + \Delta T(\Delta T \ll T)$ then
A) $\frac{\Delta T}{T} = \frac{3}{2}\frac{\Delta r}{r}$
B) $\frac{\Delta T}{T} = \frac{2}{3}\frac{\Delta r}{r}$
C) $\frac{\Delta T}{T} = \frac{\Delta r}{r}$
D) $\frac{\Delta T}{T} = - \frac{\Delta r}{r}$
Explanation
(a) Since, $T^{2} = kr^{3}$
$\Rightarrow \ \frac{2\mathrm{\Delta}T}{T} = \frac{3\mathrm{\Delta}r}{r}\ \Rightarrow \ \frac{\mathrm{\Delta}T}{T} = \frac{3}{2}\frac{\mathrm{\Delta}r}{r}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.