Question

A geostationary satellite is orbiting the earth at a height 6 R above the surface of earth, where R is the radius of the earth. The time period of another satellite at a height of 2.5 R from the surface of earth in hour is

• A. $3\sqrt{2}h$
• B. $1.5\sqrt{2}h$
• C. $6\sqrt{2}h$
• D. $12\sqrt{2}h$

Answer 1

The correct option is C $6\sqrt{2}h$

Here,

$r_1=6R+R=7R,$

$T_1=24h$

$r_2=2.5R+R=3.5R,$

$T_2=1$

$T_2={\left[\frac{R_2}{R_1}\right]}^{3/2}\times T_1=24{\left[\frac{3.5R}{7R}\right]}^{3/2}$

$=\frac{24}{2\sqrt{2}}=6\sqrt{2}h$