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JEE Main 201816 AprilOnline
Exam
JEE Main
Year
2018
Date
16 April
Mode
Online
Subject
Physics
Chapter
Gravitation

JEE Main 2018 · 16 April · Online · Physics · Gravitation

The relative uncertainty in the period of a satellite orbiting...

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:

Options

  1. A2×10−22 \times {10}^{- 2}
  2. B6×10−26 \times {10}^{- 2}
  3. C3×10−23 \times {10}^{- 2}
  4. D10−2{10}^{- 2}

Correct answer

A. 2×10−22 \times {10}^{- 2}

Step-by-step solution

From Kepler's law,

T2=4π2GMr3<br/><br/>∣∆MM∣=2∆TT=2×10−2{T}^{2} = \dfrac{4{\pi}^{2}}{GM}{r}^{3}<br /><br />\left|\dfrac{∆ M}{M}\right| = 2\dfrac{∆ T}{T} = 2 \times {10}^{- 2}
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