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The time period of a satellite revolving in a circular orbit of radius r is T. Then what is time period of another satellite revolving in the circular orbit of radius 4r?

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10T

12T

15T

answer is A.

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Detailed Solution

We know that square of time period is directly proportional to cubic square of radius of orbit in which the satellite is revolving i.e.

T^{2} \propto r^{3}

w h ere T^{2} = square of time period taken by satellite to revolve around any plan e t,

r^{3} = square cube of radius of orbit on w h ic h t h e satellite is revolving

Given, T_{1} = time period of anot h er satellite,

(\frac{T^{2}}{T_{1}^{2}}) = (\frac{r^{3}}{4 r^{3}})

\frac{T}{T_{1}} = \frac{1}{8}

T_{1} = 8 T

Therefore, time period for other satellite is 8T.

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