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MHT CET 2026 (12 May, Shift 1) · Errors in Measurement

Errors in Measurement question from MHT CET 2026 (12 May, Shift 1)

Q21MHT CET 2026 · 12 MAY · SHIFT 1Medium

Errors in Measurement

A particular physical quantity is given by X=2πabX = 2\pi\sqrt{\frac{a}{b}} and the measured value of 'a' is 4040 unit with 0.010.01 unit accuracy. The value of 'b' is 9810\frac{98}{10} unit with 11 unit accuracy. The % error in XX is nearly

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Answer: (b)

  1. X=2πa/bX = 2\pi\sqrt{a/b}, so ΔXX=12(Δaa+Δbb)\frac{\Delta X}{X} = \frac{1}{2}\left(\frac{\Delta a}{a} + \frac{\Delta b}{b}\right)
  2. Δaa=0.0140=0.025%\frac{\Delta a}{a} = \frac{0.01}{40} = 0.025\%, Δbb=19.8=10.2%\frac{\Delta b}{b} = \frac{1}{9.8} = 10.2\%
  3. ΔXX=12(10.23%)≈5.1%\frac{\Delta X}{X} = \frac{1}{2}(10.23\%) \approx 5.1\%
  4. So the answer is (b) 5%5\%.
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