The bob of a simple pendulum is made of brass and its time period is T. It is completely immersed in a liquid and is allowed to oscillate. If the density of the liquid is 1/8 th of the density of brass, what will be the time period of oscillation of the pendulum now?

The bob of a simple pendulum is made of brass and its time period is T

1.	The bob of a simple pendulum is made of brass and its time period is T. It is completely immersed in a liquid and is allowed to oscillate. If the density of the liquid is 1/8 th of the density of brass, what will be the time period of oscillation of the pendulum now?
Answer» Solution :Initial time period of the simple pendulum, `T=2pisqrt(L/g)""`[L = EFFECTIVE length of the pendulum] If m is the mass, V is the volume of the bob and d is the density of BRASS, then the apparent weight of the bob inside the liquid, `W_(1)` = W - buoyancy (weight of the DISPLACED liquid) = `Vdg-Vd/8g=7/8Vdg` If `g_(1)` is the effective acceleration DUE to gravity in the immersed condition, then `W_(1)=mg_(1)=7/8Vdgor,g_(1)=7/8(MG)/m=7/8g` `therefore` Final time period, `T_(1)=2pisqrt(L/g_(1))=2pisqrt((8L)/(7g))=sqrt(8/7)T`.