Question

Two satellites of identical masses orbit the earth at different heights. The ratio of their distances from the centre of earth is $d:1$ and the ratio of the acceleration due to gravity at those height is $g:1$. Then find the ratio of their orbital velocities.

• A. $\sqrt{\frac{g}{d}}$
• B. $\sqrt{gd}$
• C. $\sqrt{g}$
• D. $\sqrt{g}d$

Answer 1

The correct option is B $\sqrt{gd}$

Orbital velocity $=v=\sqrt{\frac{GM}{r}}$........ I

Also, $g=\frac{GM}{r^2}$

$\Rightarrow \frac{GM}{r}=gr$............. II

From equation I and II, we get

$\Rightarrow v=\sqrt{gr}$

$\Rightarrow \frac{v_1}{v_2}=\sqrt{\frac{g_1{r}_1}{g_2{r}_2}}=\sqrt{\frac{g_1{d}_1}{g_2{d}_2}}=\sqrt{gd}$

Hence correct answer is option $B$