JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement
Three students \(S_{1}, S_{2}\) and \(S_{3}\) perform an experiment for determining the acceleration due to gravity \((g)\) using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observations are as shown in the table.
| Student No. | Length of pendulum \((cm)\) | No. of oscillations \((n)\) | Total time for oscillations | Time period \((s)\) |
| \(1.\) | \(64.0\) | \(8\) | \(128.0\) | \(16.0\) |
| \(2.\) | \(64.0\) | \(4\) | \(64.0\) | \(16.0\) |
| \(3.\) | \(20.0\) | \(4\) | \(36.0\) | \(9.0\) |
- A \(4\)
- B \(3\)
- C \(1\)
- D same in all
Answer & Solution
Correct Answer
(C) \(1\)
Step-by-step Solution
Detailed explanation
\(T=2 \pi \sqrt{\frac{\ell}{g}} \Rightarrow g=\frac{4 \pi^{2} \ell}{T^{2}}\) \(\frac{\Delta g}{g}=\frac{\Delta \ell}{\ell}+\frac{2 \Delta T}{T}\) \(\Delta T=\frac{\text { least count of time }\left(\Delta T_{0}\right)}{\text { number of oscillations(n) }}\)…
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