Question

A long capillary tube of radius of 0.2mm is placed vertically inside a beaker of water. If the surface tension of water is $7.2\times {{10}^{-2}}N/m$ and the angle of contact between glass and water is zero, then determine the height of the water column in the tube.
A. 3 cm
B. 9 cm
C. 7 cm
D. 5 cm

Answer 1

Hint: At first we need to note all the possible values that are given in the question. Now after that we must write the equation for water rise in the capillary tube. Then we will have to find the value of $\cos \theta $, and apply it in the formula, then place all the required values and find the result that is needed.

Complete answer:
We know that the radius of the tube is r = 0.2 mm.
We know that the surface tension of the water is $7.2\times {{10}^{-2}}N/m$.
And we also know that the angle of contact is zero.
Now, according to the question
We know that the equation for water column rise in the capillary tube is,
$h=\dfrac{2T\cos \theta }{r\rho g}$,
Now we know that angle of contact is zero, so
$\cos 0=1$
$h=\dfrac{2T}{r\rho g}$,
Now, on substituting the values,
$h=\dfrac{2\times 7.2\times {{10}^{-2}}}{0.2\times {{10}^{-3}}\times {{10}^{3}}\times 9.8}$,
Now, on solving the above equation, h=0.07m or 7cm

So, the correct answer is “Option C”.

Note:
In the equation of water column rise in capillary tube $h=\dfrac{2T\cos \theta }{r\rho g}$, T is the surface tension of the water, ‘r’ is the radius of the capillary tube, $'\rho '$ is the density of the liquid in the capillary tube, and g is the acceleration due to gravity. Students must note that all the values given are in the same unit or not if they are not in the same unit students must always bring them to a standard unit before calculating with them. Like we know that the radius was 2mm so we converted it into meters and solved the equation. In the last part we got the answer in meters but the options were given in centimeters so we converted it to centimeters.