Question

A simple pendulum with a brass bob has a time period $T.$ The bob is now immersed in a non viscous fluid and oscillated$.$ If the density of liquid is $1/8$ of the brass$.$ Find the time period of simple pendulum

• A. $7g/8$
• B. $6g$
• C. $4g/3$
• D. $9g/7$

Answer 1

The correct option is A $7g/8$

Density of the liquid $=\left(1/8\right)\rho$

Where $\rho$ be the density of the brass

We know that time period of the pendulum is$:$

Assuming the density of the object is greater than the density of the liquid $i.e,$ $\rho >{\rho }^{\prime }$

$($if the density of the object is less than the density of the liquid then the object would not sustain oscillation even if it moves at all and it would soon come to rest$).$

Now$,$ if the density of the object is $\rho$ and it is made to oscillate in a liquid of density $\rho /8$ then the effective value of acceleration due to gravity acting on the bob will be

$g^{\prime }=g$ $(1-$ density of sphere/density of liquid) $=g(1-1/8)=7g/8$

Hence,

option $\left(A\right)$ is correct answer.