First slide

Surface tension

Question

Three liquids of densities $ρ_{1}, ρ_{2} a n d ρ_{3}$ (with $ρ_{1}, ρ_{2} > ρ_{3}$ ), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact $θ_{1}, θ_{2} a n d θ_{3}$ obey

Moderate

A

$\frac{π}{2} > θ_{1} > θ_{2} > θ_{3} \geq 0$
B

$0 \leq θ_{1} < θ_{2} < θ_{3} < \frac{π}{2}$
C

$\frac{π}{2} < θ_{1} < θ_{2} < θ_{3} < π$
D

$π > θ_{1} > θ_{2} > θ_{3} > \frac{π}{2}$

Solution

$Capillary rise, h = \frac{2 T \cos θ}{ρ g r}$
$For given value of T and r, h \propto \frac{\cos θ}{ρ}$
$Also, h_{1} = h_{2} = h_{3} or, \frac{\cos θ_{1}}{ρ_{1}} = \frac{\cos θ_{2}}{ρ_{2}} = \frac{\cos θ_{3}}{ρ_{3}}$
$Since, ρ_{1} > ρ_{2} > ρ_{3}, so \cos θ_{1} > \cos θ_{2} > \cos θ_{3}$
$\begin{array}{l} For 0 \leq θ < \frac{π}{2}, θ_{1} < θ_{2} < θ_{3} \\ Hence, 0 \leq θ_{1} < θ_{2} < θ_{3} < \frac{π}{2} \end{array}$

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