Verified Solution • 2025–26 Session moderate

QJEEM24Ph6be3: JEE Main 2024 Physics - Class 11 JEEM24Ph6be3 Solution: The measured value of the length of a simple pendulum is with…

The measured value of the length of a simple pendulum is 20 cm20 \mathrm{~cm} with 2 mm2 \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 N%\mathrm{N} \% . The value of N\mathrm{N} is:

Multiple Choice Options

  • A 6
  • B 5
  • C 4
  • D 8

Step-by-Step Verified Solution

amp;T=2πℓgamp;g=4π2ℓT2amp;Δgg=Δℓℓ+2ΔTTamp;=0.220+2(140)amp;=1.220\begin{aligned}& \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{1.2}{20}\end{aligned}

Percentage change =1.220×100=6%=\frac{1.2}{20} \times 100=6 \%

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