Given that, a bob of mass m suspended by a thread of length l undergoes SHM with time period,
T1=T=2π√ ...(i)
In liquid, effective gravity,
geff=g() where, ρ = density of liquid
and σ = density of body (bob).
Given,
ρ= ⇒σ=4ρ Substituting this value, we get
geff=g()= Now, the new time period of pendulum in liquid is
T′=2π√ ...(ii)
Here,
l′=l+= Substituting the values in Eq. (ii), we get
T′=2π√× =(2π√) ⇒T′= [from Eq. (i)]