Gravitation

JEE Main level, single correct, medium

220 of 223

Question 220 of 223

The relative uncertainty in the period of a satellite orbiting around the earth is 10−2{10}^{-2} . If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is:

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Answer: (A) 2×10−22\times {10}^{-2}

From Kepler's law,

T2=4π2GMr3{T}^{2}=\dfrac{4{\pi }^{2}}{GM}{r}^{3}

∣∆MM∣=2∆TT=2×10−2\left|\dfrac{∆M}{M}\right|=2\dfrac{∆T}{T}=2\times {10}^{-2}

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