Question

A liquid rises to a height of $1.8cm$ in a glass capillary ‘$A$’. Another glass capillary ‘$B$’ having diameter $90\%$ of capillary ‘$A$’ is immersed in the same liquid. The rise of liquid in capillary ‘$B$’ is

• A. $1.4cm$
• B. $1.8cm$
• C. $2.0cm$
• D. $2.2cm$

Answer 1

Answer: (C)

Height of liquid in a capillary tube, $h=\frac{2S\cos \theta }{rpg}$
where, $S=$ surface tension
$\rho =$ density of the liquid
$r=$ radius of the capillary tube
For capillary $A,h_A=\frac{2S\cos \theta }{r_A\rho g}..(i)$
For capillary $B,h_B=\frac{2S\cos \theta }{r_B\rho g}...(ii)$
From Eqs. (i) and (ii), we get
$h_A{r}_A=h_B{r}_B$
$\Rightarrow (1.8cm)\left(r_A\right)=\left(h_B\right)\left(\frac{90}{100}\times r_A\right)$
or $(1.8cm)=h_B\times \frac{9}{10}$
or $h_B=\frac{10}{9}\times 1.8cm=2cm$