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JEE Main 2018 (16 Apr, Shift 1) · Errors in Measurement

Errors in Measurement question from JEE Main 2018 (16 Apr, Shift 1)

Q99JEE Main 2018 · 16 APR · SHIFT 1Medium

Errors in Measurement

The relative uncertainty in the period of a satellite orbiting around the earth is 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: (b)

  1. Kepler's law: T2=4π2r3GM⇒M=4π2r3GT2T^2 = \frac{4\pi^2 r^3}{GM} \Rightarrow M = \frac{4\pi^2 r^3}{GT^2}.
  2. With Δr\Delta r negligible: ΔMM=2ΔTT=2×10−2\frac{\Delta M}{M} = 2\frac{\Delta T}{T} = 2 \times 10^{-2}
  3. So the answer is (b) 2×10−22 \times 10^{-2}.
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