First slide

Applications of SHM

Question

A simple pendulum oscillating in air has period T. The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is ${(\frac{10}{16})}^{t h}$ of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is

Moderate

A

$T \sqrt{\frac{1}{6}}$
B

$4 T \sqrt{\frac{1}{6}}$
C

$2 T \sqrt{\frac{1}{14}}$
D

$4 T \sqrt{\frac{1}{15}}$

Solution

$\begin{array}{rcl} t i m e p e r i o d o f a s i m p l e p e n d u l u m i s T & = & 2 π \sqrt{\frac{l}{g}} \\ \Rightarrow & Tα \frac{1}{\sqrt{g}}, here 2 π, l are constants \\ T \sqrt{g} & = & T^{1} \sqrt{g^{1}} - - - - (1) \\ v a r i a t i o n i n a c c e l e r a t i o n d u e t o g r a v i t y i n s i d e l i q u i d i s g^{1} & = & g (1 - \frac{d_{l i q u i d}}{d_{b o d y}}) \\ g^{1} & = & g (1 - \frac{10}{16}) = g (\frac{6}{16}) \\ ∴ T \sqrt{g} & = & T^{1} \sqrt{g \frac{6}{16}} \\ T & = & \frac{T^{1} \sqrt{6}}{4} \\ t i m e p e r i o d i n s i d e l i q u i d i s ∴ T^{1} & = & \frac{4 T}{\sqrt{6}} s \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App