Question

If the angular velocity of a planet about its own axis is halved, the distance of geostationary satellite of this planet from the cent of the planet will become :

• A. $(2{)}^{1/3}$ times
• B. $(2{)}^{3/2}$ times
• C. $(2{)}^{2/3}$ times
• D. 4 times

Answer 1

Answer: (B)

$(2{)}^{3/2}$ times

Lets consider,

${\omega }_1=\omega$ angular velocity

${\omega }_2=\frac{\omega }{2}$

$r=$ distance between geostationary satellites.

The Time period, $T\propto r^{3/2}$

$\frac{2\pi }{\omega }\propto r^{3/2}$

$\omega \propto r^{-3/2}$. . . . .(1)

$\frac{{\omega }_2}{{\omega }_1}\propto (\frac{r_2}{r_1}{)}^{-3/2}$

$\frac{1}{2}\propto (\frac{r_2}{r_1}{)}^{-3/2}$

$r_2=(2{)}^{3/2}{r}_1$

The correct option is B.