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

$T i m e p e r i o d o f a s i m p l e p e n d u l u m o f l e n g t h l, a c c e l e r a t i o n d u e t o g r a v i t y g i s T=2π \sqrt{\frac{l}{g}}________(1) T i m e p e r i o d o f a s i m p l e p e n d u l u m i n s i d e l i q u i d i s, T^{1} =2π \sqrt{\frac{l}{g (1- \frac{d_{l}}{d_{s}})}} g i v e n l i q u i d o f d e n s i t y o n e - e i g h t h o f t h e d e n s i t y o f t h e m a t e r i a l o f t h e b o b T^{1} =2π \sqrt{\frac{l}{g (1- \frac{1}{8})}} T^{1} =2π \sqrt{\frac{l}{g (\frac{7}{8})}}(2) e q u a t i o n (2) \div (1) T^{1} =2π \sqrt{\frac{8l}{7g}}___T=2π \sqrt{\frac{l}{g}} \Rightarrow T^{1} = \sqrt{\frac{8}{7}} T$

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