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Motion In Straight Line

Question
CBSEENPH11017792

Two satellites are revolving in circular orbits of radius R and 4R around a planet. What is the ratio of the time period?

Solution
Given, two satellites are revolving in a circular orbits or radius R and 4R.
According to Kepler’s law of planetary motion, 
                        straight T squared proportional to straight R cubed 
Therefore, the ratio of the time period is given by,
                    straight T subscript 1 squared over straight T subscript 2 squared equals fraction numerator straight R cubed over denominator left parenthesis 4 straight R right parenthesis cubed end fraction equals 1 over 64 
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#6 {main}</pre> 
i.e., T1: T2 is 1: 8