First slide

Applications of SHM

Question

A simple pendulum has time period 3 seconds. The pendulum is completely immersed in a non viscous liquid whose density is ${\frac{1}{10}}^{th}$ of that of the material of the bob. Then time period of that pendulum is

Moderate

A

$\sqrt{3}$ seconds
B

3 seconds
C

$\frac{3}{\sqrt{10}}$ seconds
D

3.162seconds

Solution

given ${density of liquid =d}_{l} = \frac{1}{10} d_{b} {;density of the pendulum=d}_{b}$
$time period of simple pendulum =T=2π \sqrt{\frac{l}{g}} =3 given---(1) ; l=length of the pendulum; g= acceleration due to gravity$ =3------(1)
$time period of simple pendulum i n s i d e l i q u i d T^{1} =2π \sqrt{\frac{l}{g (1 - \frac{d_{l}}{d_{b}})}}$
$T^{1} =2π \sqrt{\frac{l}{g (1 - \frac{1}{10})}} = \sqrt{\frac{l (10)}{g9}}$
$T^{1} =2π \sqrt{\frac{l}{g}} (\sqrt{\frac{10}{9}}) substitute eqn(1)$
$T^{1} =3 \times \frac{\sqrt{10}}{3} = \sqrt{10}$ =3.162 seconds.=time period of pendulum immersed in liquid

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