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 heights is $g:1$. Then the ratio of their orbital velocities is _______

• A. $\sqrt{dg}:1$
• B. $\sqrt{dg}:2$
• C. $\sqrt{dg}:11$
• D. $\sqrt{dg}:3$

Answer 1

The correct option is A $\sqrt{dg}:1$

Let mass of earth be $m$ and radius of the earth is $r$. Ratio of their heights from center of the earth is $d:1$ means if $2nd$ body is at $r$ distance from the body is at $3rd$ distance from center of the earth similarly of those heights is $g:1$ means that acceleration due to gravity for $1st$ body is $g$ then acceleration due to gravity for $2nd$ body is orbital velocity $=\sqrt{gr}$

Where $g$ is the acceleration due to gravity experienced by object at $r$ distance of object from the center of the earth.

Ratio of orbital velocities $=\frac{\sqrt{g.rd}}{\sqrt{1.r}}=\frac{\sqrt{gd}}{1}$

$=\sqrt{gd}:1$

$=\sqrt{dg}:1$

Option $\left(1\right)$ correct.