Question

The capillaries shown in figure. have inner raii 0.5 mm, 1.0 mm and 1.5 mm respectively. The liquid in the beaker is water. Find the heights of water level in the capillaries. The surface tension of water is $7.5\times {10}^{-2}N{m}^{-1}$.

Answer 1

(a) T = $7.5\times {10}^{-2}N/m,cos\theta =1$

$h_A=\frac{2Tcos\theta }{r_A\rho g}$

$=\frac{2\times 7.5\times {10}^{-2}}{5\times {10}^{-3}\times 1000\times 10}$

= $3\times {10}^{-2}m=3cm$

(b) $h_B=\frac{2Tcos\theta }{r_B\rho g}$

= $\frac{2\times 7.5\times {10}^{-2}}{5\times {10}^{-3}\times {10}^3\times 10}$

= $15\times {10}^{-3}m=1.5cm$

(c) $h_0=\frac{2Tcos\theta }{r_B\rho g}$

= $\frac{2\times 7.5\times {10}^{-2}}{1.5\times {10}^{-3}\times {10}^3\times 10}$

= $\frac{15}{1.5}\times {10}^{-3}={10}^{-2}m=1cm$

The height of $H_{2}0$ level in A, B, C capillaries are 3 cm 1.5 cm and 1 cm respectively.