JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement
The measured value of the length of a simple pendulum is \(20 \mathrm{~cm}\) with \(2 \mathrm{~mm}\) accuracy. The time for \(50\) oscillations was measured to be \(40\) seconds with \(1\) second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is \(\mathrm{N} \%\). The value of \(\mathrm{N}\) is _______.
- A \(4\)
- B \(8\)
- C \(6\)
- D \(5\)
Answer & Solution
Correct Answer
(C) \(6\)
Step-by-step Solution
Detailed explanation
\(\mathrm{T}=2 \pi \sqrt{\frac{\ell}{\mathrm{g}}}\) \(\mathrm{g}=\frac{4 \pi^2 \ell}{\mathrm{T}^2}\) \(\frac{\Delta \mathrm{g}}{\mathrm{g}}=\frac{\Delta \ell}{\ell}+\frac{2 \Delta \mathrm{T}}{\mathrm{T}}\) \(=\frac{0.2}{20}+2\left(\frac{1}{40}\right)\) \(=\frac{0.3}{20}\)…
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