Question

The time period of a satellite of earth is $5$ hours. If the separation between the earth and the satellite is increased to $4$ times the previous value, the new time period will become

• A. 10 hours
• B. 80 hours
• C. 40 hours
• D. 20 hours

Answer 1

Answer: (C)

40 hours

Answer 2

Time period of a satellite is the time taken by satellite to go once around the earth. $T =2 \pi \sqrt{\frac{ r ^{3}}{ MG }}$,
so $T$ depends on $r ^{\frac{3}{2}}$.
so if $r$ is increased to $4$ times then time period will be $8$ times
$\left(4^{\frac{3}{2}}=8\right)$.