The lower end of a capillary tube is dipped into water and it is observed that the water in capillary tube rises by 7.5cm. Find the radius of the capillary tube used, if surface tension of water is $7.5 \times 10^{- 2} N m^{- 1} .$ Angle of contact between water and glass is $0^{o}$ and acceleration due to gravity is $10 m s^{- 2}$

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0.2 cm

0.4 mm

0.2 mm

0.1 cm

answer is D.

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Detailed Solution

Given, capillary rise, H = 7.5 cm = $7.5 \times 10^{- 2} c m$
Surface tension, T = $7.5 \times 10^{- 2} N m^{- 1}$
Angle of contact $θ = 0^{o}$
Acceleration due to gravity = 10 $m s^{- 2}$
Let radius of capillary tube be R
Density of water $ρ = 1000 k g / m^{3}$
Since, $H = \frac{2 T \cos θ}{ρ g R}$
$\Rightarrow R = \frac{2 T \cos θ}{ρ g H} = \frac{2 \times 7.5 \times 10^{- 2}}{1000 \times 10 \times 7.5 \times 10^{- 2}} = 2 \times 10^{- 4} m = 0.2 m m$