A cylindrical isotropic solid of coefficient of linear expansion α and density ρ floats in a liquid of coefficient of volume expansion γ and density d as shown in the diagram
Column I | Column II | ||
(a) | volume of cylinder inside the liquid remains constant | (p) | γ = 0 |
(b) | volume of cylinder outside the liquid remains constant | (q) | γ = 2α |
(c) | Height of cylinder outside the liquid remains constant | (r) | γ = 3α |
(d) | Height of cylinder inside the liquid remain constant | (s) | γ = (2α + α ) |
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
– (p); – (r); – (s); – (q)
Sol. Buoyant force = Mg = constant = 
V sub = 
.
volume of displace fluid = constant
∴ density of fluid must be constant.
(V solid – V sub ) = constant
⇒ 
= constant V × 3 α × Δ T = 
γ = 
Ah in d liquid = A (h in +h out ) ρ solid = M (mass of solid)
h out = 
– h in = 
– 
= constant
– 
= 
γ = 2 α + α 
Ah in d liquid g = Buoyant force = constant = Mg
A 0 (1 + 2 α Δ T) h in 
= constant
h in = 
(1 + ( γ – 2 α ) Δ T)
γ = 2 α
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