A coaxial cylinder made of glass is immersed in a liquid of surface tension S . The radius of the inner and outer surface of the cylinder are R1 and R2 respectively. Height till which liquid will rise is (Density of liquid is ρ )

Question

A coaxial cylinder made of glass is immersed in a liquid of surface tension S . The radius of the inner and outer surface of the cylinder are R1 and R2 respectively. Height till which liquid will rise is (Density of liquid is ρ ) (A) (2 S/R2 ρ g) (B) (2 S/R1 ρ g) (C) (S/(R2 - R1) ρ g) (D) (2 S/(R2 - R1) ρ g)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-mgs9cev88sol.png" /> Net upward force = 2π R2S + 2π R1 S contact angle=0° ∴ Capillary rise is given by h=(2 π S (R1 + R2)/π (R22 - R12) ρ g) = (2 S/(R2 - R1) ρ g)

Q. A coaxial cylinder made of glass is immersed in a liquid of surface tension $S$ . The radius of the inner and outer surface of the cylinder are $R_{1}$ and $R_{2}$ respectively. Height till which liquid will rise is (Density of liquid is $ρ$ )

$\frac{2 S}{R _{2} ρ g}$

$\frac{2 S}{R _{1} ρ g}$

$\frac{S}{( R _{2} - R _{1} ) ρ g}$

$\frac{2 S}{( R _{2} - R _{1} ) ρ g}$

Net upward force
$= 2 π R_{2} S + 2 π R_{1} S co n t a c t an g l e = 0^{\circ}$
$∴$ Capillary rise is given by
$h = \frac{2 π S ( R _{1} + R _{2} )}{π ( R _{2}^{2} - R _{1}^{2} ) ρ g}$
$= \frac{2 S}{( R _{2} - R _{1} ) ρ g}$

Q. A coaxial cylinder made of glass is immersed in a liquid of surface tension S . The radius of the inner and outer surface of the cylinder are R1​ and R2​ respectively. Height till which liquid will rise is (Density of liquid is ρ )

R2​ρg2S​

R1​ρg2S​

(R2​−R1​)ρgS​

(R2​−R1​)ρg2S​