Time Period Ratio of Satellites with Different Masses – Rankers Physics
Topic: Gravitation
Subtopic: Keplers Law

Time Period Ratio of Satellites with Different Masses

A satellite A of mass $m$ is at a distance of $r$ from the surface of the earth. Another satellite B of mass $2m$ is at a distance of $2r$ from the earth's centre. Their time periods are in the ratio of:

(1993)

$1:2$
$1:16$
$1:32$
$1:2\sqrt{2}$

Solution:

Time period of a satellite is independent of its mass. Assuming the distance $r$ for satellite A was intended to be from the centre (a standard typo in this question format), $r_A = r$ and $r_B = 2r$. Their time period ratio $\frac{T_A}{T_B} = \left(\frac{r_A}{r_B}\right)^{3/2} = \left(\frac{1}{2}\right)^{3/2} = 1:2\sqrt{2}$.

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