Question

The time period of a geostationary satellite is 24 h, at a height 6R (R is radius of earth) from surface of earth. The time period of another satellite whose height is 2.5 R from surface will be,

• A. 6 $\sqrt{ 2}$ h
• B. 12 $\sqrt{ 2}$ h
• C. $\frac{24}{2.5} h$
• D. $\frac{12}{2.5} h$

Answer 1

The Correct Option is A

Kepler�s Third Law :- $T \propto r^{3/2}$ $\frac{T_{2}}{T_{1}} = \left(\frac{r_{2}}{r_{1}}\right)^{3/2}$ $=\left(\frac{R + 2.5R}{R + 6R}\right)^{3/2} = \frac{1}{2\sqrt{2}} $ $\Rightarrow T_{2} = \frac{24}{2\sqrt{2} }= 6\sqrt{2}$ hours