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  4. Suppose radius of the moons orbit around the earth is doubled. Its period around the earth will become :

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Q. Suppose radius of the moons orbit around the earth is doubled. Its period around the earth will become :

Rajasthan PMTRajasthan PMT 2005

Solution:

According to Keplers law $T^{2} \propto R^{3}$
(Here : R is orbital radius and T is time period)
Now according to question when orbital radius is doubled, then period will be
$\frac{T_{1}}{T_{2}}=\left(\frac{R}{2 R}\right)^{3 / 2}$
$T_{2}=2^{3 / 2} T_{1}$
(Here $\left.: R_{1}=R, R_{2}=2 R\right)$
Hence, the time period will become $ {{2}^{3/2}} $ times.