A simple pendulum of length l and mass m of bob is suspended in a car that is travelling with a cons

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13.Oscillations

hard

A simple pendulum of length $l$ and mass $m$ of the bob is suspended in a car that is travelling with a constant speed $v$ around a circular path of radius $R$. If the pendulum undergoes oscillations with small amplitude about its equilibrium position, the frequency of its oscillations will be

A

$\frac{1}{{2\pi }}\,\sqrt {\frac{g}{l}} $

B

$2\pi \,\sqrt {\frac{l}{g}} $

C

$\frac{1}{{2\pi }}\,\sqrt {\frac{{\left( {{g^2} + \frac{{{v^4}}}{{{R^2}}}} \right)}}{l}} $

D

$\frac{1}{{2\pi }}\,\sqrt {\frac{{{{\left( {{g^2} + \frac{{{v^4}}}{{{R^2}}}} \right)}^{\frac{1}{2}}}}}{l}} $

Solution

$\because g_{e f f}=\sqrt{g^{2}+\left(\frac{v^{2}}{R}\right)^{2}}$

$T=2 \pi \sqrt{\frac{\ell}{\sqrt{g^{2}+\frac{v^{4}}{R^{2}}}}}$

Standard 11

Physics

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