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Motion In Straight Line

Question
CBSEENPH11017783

A satellite revolves in an orbit close to the surface of planet of density 5800 kg/ m3. Find the time period of revolution of the satellite.

Solution
The time period of the satellite revolving close to the surface of planet is,
                      straight T equals 2 straight pi square root of straight R cubed over GM end root 
where M is the mass of the planet.
The mass of planet, M equals 4 over 3 πR cubed straight rho 
Therefore,
 Time period, straight T equals 2 straight pi square root of fraction numerator 3 straight R cubed over denominator straight G cross times 4 πρR cubed end fraction end root space equals space square root of fraction numerator 3 straight pi over denominator Gρ end fraction end root
Here, we have
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Therefore,
 straight T equals square root of fraction numerator 3 cross times 22 over denominator 7 cross times 6.67 cross times 10 to the power of negative 11 end exponent cross times 5800 end fraction end root space equals space 4937 straight s, is the required time period of the revolution of satellite.