JEE Mains · Physics · STD 11 - Oscillations
- JEE Mains 2019
- Hard
- MCQ
A simple pendulum oscillating in air has period \(T.\) The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is \(\frac {1}{16}\) of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \(4T\sqrt {\frac {1}{15}}\)
Step-by-step Solution
Detailed explanation
For a simple pendulum \(\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{L}}{\mathrm{g}_{\mathrm{err}}}}\)
Situation \(1\): when pendulum is in air \(\rightarrow g_{\text {eff }}=g\)
Situation \(2\) :when pendulum is in liquid
\(\rightarrow g_{e f}=g\left(1-\frac{\rho_{\text {liquid }}}{\rho_{\text {body }}}\right)=g\left(1-\frac{1}{16}\right)=\frac{15 g}{16}\)
So, \(\frac{\mathrm{T}^{\prime}}{\mathrm{T}}=\frac{2 \pi \sqrt{\frac{\mathrm{L}}{15 \mathrm{g} / 16}}}{2 \pi \sqrt{\frac{\mathrm{L}}{\mathrm{g}}}}\)
\(\Rightarrow \mathrm{T}^{\prime}=\frac{4 \mathrm{T}}{\sqrt{15}}\)
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