Question

Two satellites are revolving round the earth in circular orbits of radii in the ratio $1:2$. Their orbital velocities are in the ratio of:

• A. $1:2$
• B. $\sqrt{2}:1$
• C. $2\sqrt{2}:1$
• D. $8:1$

Answer 1

The correct option is B $\sqrt{2}:1$

Orbital speed is given by, $v=\sqrt{\frac{GM}{r}}$

$\Rightarrow v\propto \sqrt{\frac{1}{r}}$

$\Rightarrow \frac{v_1}{v_2}=\sqrt{\frac{r_2}{r_1}}=\sqrt{\frac{2}{1}}$; $($ since $\frac{r_1}{r_2}=\frac{1}{2}$ $)$

$\Rightarrow v_1:v_2=\sqrt{2}:1$