Three liquids of densities p₁,p₂ and p₃ $\left(\mathrm{with} {\mathrm{p}}_1>{\mathrm{p}}_2>{\mathrm{p}}_3\right)$, having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact ${\mathrm{\theta }}_1, {\mathrm{\theta }}_2 \mathrm{and} {\mathrm{\theta }}_3$ obey

The rise of a liquid in a capillary tube is

$\mathrm{h}=\frac{2\mathrm{Tcos\theta }}{\mathrm{r\rho g}}\Rightarrow \mathrm{cos\theta }=\frac{\mathrm{hr\rho g}}{2\mathrm{T}}$

h, T, and r are constants for all three liquids at this point.

${\mathrm{\rho }}_1>{\mathrm{\rho }}_2>{\mathrm{\rho }}_3$

$\therefore {\mathrm{cos\theta }}_1>{\mathrm{cos\theta }}_2>{\mathrm{cos\theta }}_3$

${\mathrm{\theta }}_1<{\mathrm{\theta }}_2<{\mathrm{\theta }}_3$

Angles of contact will be acute since the liquid is rising in all three capillaries at this point.

$0⩽{\mathrm{\theta }}_1<{\mathrm{\theta }}_2<{\mathrm{\theta }}_3<\frac{\mathrm{\pi }}{2}.$

Hence the correct answer is $0⩽{\mathrm{\theta }}_1<{\mathrm{\theta }}_2<{\mathrm{\theta }}_3<\frac{\mathrm{\pi }}{2}.$