If the surface tension of water is 0.06 N/m, then the capillary rise in a tube of diameter 1mm is (θ = 0° )

Correct Answer: The correct option is 2.44 cm.

Step-by-Step Explanation:

Capillarity is the phenomenon of rise or fall of a liquid surface in a small tube relative to the adjacent general level of liquid. The height of capillary rise or fall is given by the formula:

$h=\frac{4Tcos\theta }{\rho gd}$
where:
• $h$ is the capillary rise (in meters)
• $T$ is the surface tension of the liquid ($0.06\text{N/m}$)
• $\theta$ is the angle of contact ($0°$)
• $\rho$ is the density of the liquid (for water, $\rho =1000{\text{kg/m}}^3$)
• $g$ is the acceleration due to gravity ($9.8{\text{m/s}}^2$)
• $d$ is the diameter of the tube ($1\text{mm}={10}^{-3}\text{m}$)

Substitute the given values into the formula:

$h=\frac{4\times 0.06\times cos(0°)}{1000\times 9.8\times {10}^{-3}}$

Since $cos(0°)=1$ and $1000\times {10}^{-3}=1$, the expression simplifies to:

$h=\frac{0.24}{9.8}$

Calculate the value of $h$:

$h\approx 0.02449\text{m}$

Convert the height from meters to centimeters by multiplying by 100:

$h\approx 2.449\text{cm}\approx 2.44\text{cm}$