First slide

Applications of SHM

Question

A simple pendulum has a time period 'T' in vacuum. It’s time of period when it is completely immersed in a liquid of density one-eighth of the density of the material of the bob is

Moderate

A

$\sqrt{\frac{7}{8}} T$
B

$\sqrt{\frac{5}{8}} T$
C

$\sqrt{\frac{3}{8}} T$
D

$\sqrt{\frac{8}{7}} T$

Solution

$time period of simple pendulum isT=2π \sqrt{\frac{l}{g}} ---(1) time period of simple pendulum w h e n i m m e r s e d i n l i q u i d i s T^{1} =2π \sqrt{\frac{l}{g (1- \frac{d_{liquid}}{d_{b o d y}})}} d_{liquid} {= density of liquid , d}_{b o d y} =density of body or oscillator, s u b s t i t u t e t h e g i v e n v a l u e s T^{1} =2π \sqrt{\frac{l}{g (1- \frac{1}{8})}} T^{1} =2π \sqrt{\frac{l}{g (\frac{7}{8})}} T^{1} =2π \sqrt{\frac{8l}{7g}} s u b s t i t u t e (1) i n a b o v e e q u a t i o n o r d i v i d e e q u a t i o n s o f T a n d T^{1} T^{1} = \sqrt{\frac{8}{7}} T$

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