If water rises in a capillary tube up to $3 \, cm$,what is the diameter of the capillary tube? (Surface tension of water $T = 7.2 \times 10^{-2} \, N/m$,density $\rho = 10^3 \, kg/m^3$,$g = 10 \, m/s^2$)

Two narrow bores of diameters $3.0 \;mm$ and $6.0 \;mm$ are joined together to form a $U$-tube open at both ends. If the $U$-tube contains water,what is the difference (in $mm$) in its levels in the two limbs of the tube? Surface tension of water at the temperature of the experiment is $7.3 \times 10^{-2} \;N m^{-1}$. Take the angle of contact to be zero and density of water to be $1.0 \times 10^{3} \;kg m^{-3}$ $(g = 9.8 \;m s^{-2})$.

$A$ capillary tube made of glass with a radius of $0.15\, mm$ is dipped vertically in a beaker filled with methylene iodide (surface tension $= 0.05\, N m^{-1}$,density $= 667\, kg m^{-3}$),which rises to a height $h$ in the tube. It is observed that the two tangents drawn from the liquid-glass interfaces (from opposite sides of the capillary) make an angle of $60^{\circ}$ with one another. Then $h$ is close to $...... m$ $(g = 10\, m s^{-2})$

$A$ capillary tube is taken from the Earth's surface to the Moon's surface. What happens to the rise of the liquid column on the Moon's surface? (Acceleration due to gravity on the Earth's surface is six times that of the Moon's surface.)

Water rises to a height of $16.3 \,cm$ in a capillary tube. If the tube is cut at a height of $12 \,cm$ above the water level,what will happen?

Water rises in a capillary tube kept vertically on the surface of the Earth to a height $h$. Choose the false statement regarding capillary rise from the following $:-$