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  4. 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

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Q. 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

BITSATBITSAT 2019

Solution:

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
$\left(4^{\frac{3}{2}}=8\right)$.