The metallic bob of a simple pendulum has the relative density . … - Vidyadip

MCQ

The metallic bob of a simple pendulum has the relative density $\rho$. The time period of this pendulum is $T$. If the metallic bob is immersed in water, then the new time period is given by

A
$T\frac{{\rho - 1}}{\rho }$
B
$T\frac{\rho }{{\rho - 1}}$
C
$T\sqrt {\frac{{\rho - 1}}{\rho }} $
✓
$T\sqrt {\frac{\rho }{{\rho - 1}}} $

✓

Answer

Correct option: D.

$T\sqrt {\frac{\rho }{{\rho - 1}}} $

d
(d) When the bob is immersed in water its effective weight = $\left( {mg - \frac{m}{\rho }g} \right) = mg\,\left( {\frac{{\rho - 1}}{\rho }} \right)$

$\therefore {g_{eff}} = g\,\left( {\frac{{\rho - 1}}{\rho }} \right)$

$\frac{{T'}}{T} = \sqrt {\frac{g}{{{g_{eff}}}}} $

$\frac{{T'}}{T} = \sqrt {\frac{\rho}{{\rho -1}}} $

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