The correct option is A
Given, height of cylinder (h)=1 m=100 cm
From the data given in the question we can say that,
Length of cylinder submerged in water at 0∘C
is l1=80 cm
Length of cylinder submerged in water at 4∘C
is l2=79 cm
Pictorial representation of situation given in the question is shown below.
From Archimedes principle, we can say that
Buoyant force = weight of the fluid displaced.
and for vertical equilibrium of cylinder,
: Vsρsg=Vfρfg ⇒ρsρf=VfVs=Height of cylinder immersedTotal height of cylinder ⇒ρsρf=l1h=80100 ....(1)
Similarly, at 4∘C
is the new density of fluid and V′f
is the new volume displaced ⇒ρsρ′f=Height of cylinder immersedTotal height of cylinder ⇒ρsρ′f=l2h=79100 ...........(2)
So, from (1)
and (2) ρ′fρf=8079=1.01
Thus, option (a) is the correct answer.