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JEE Main 2024 (6 Apr, Shift 1) · Errors in Measurement

Errors in Measurement question from JEE Main 2024 (6 Apr, Shift 1)

Q62JEE Main 2024 · 6 APR · SHIFT 1Medium

Errors in Measurement

To find the spring constant (k)(k) of a spring experimentally, a student commits 2%2\% positive error in the measurement of time and 1%1\% negative error in measurement of mass. The percentage error in determining value of kk is:

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Answer: (a)

  1. Spring-mass system: T=2πm/k⇒k=4π2mT2T = 2\pi\sqrt{m/k} \Rightarrow k = \frac{4\pi^2 m}{T^2}.
  2. Δkk=Δmm−2ΔTT=(−1%)−2(+2%)=−5%\frac{\Delta k}{k} = \frac{\Delta m}{m} - 2\frac{\Delta T}{T} = (-1\%) - 2(+2\%) = -5\%
  3. Magnitude of error in kk is 5%5\%.
  4. So the answer is (a) 5%5\%.
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