Gravitation

JEE Main level, single correct, medium

210 of 223

Question 210 of 223

The time period of a satellite revolving around earth in a given orbit is 77 hours. If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be

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Answer: (A) 36hours36hours

From Kepler's Third Law(The Law of Periods), we know
T2∝R3⇒T22T12=(R2R1)3=(3RR)3{T}^{2}\propto {R}^{3}\Rightarrow \dfrac{{T}_{2}^{2}}{{T}_{1}^{2}}={\left(\dfrac{{R}_{2}}{{R}_{1}}\right)}^{3}={\left(\dfrac{3R}{R}\right)}^{3}
Therefore, T2=27T1{T}_{2}=\sqrt{27}{T}_{1}
=5.19×7≈36hours=5.19\times 7\approx 36hours

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