The heat evolved for the rise of water when one end of the capillary tube of radius $r$ is immersed vertically into water is (Assume surface tension $= T$ and density of water to be $\rho$)

Which of the following statements is false?

$A$ capillary tube of radius $r$ is immersed in water and water rises in it to a height $h$. The mass of the water in the capillary tube is $m$. Another capillary of radius $2r$ is immersed in water. The mass of water that will rise in this tube is

Water rises against gravity in a capillary tube when its one end is dipped into water because

In a capillary tube experiment,a vertical $20 \,cm$ long capillary tube is dipped in water. The water rises up to a height of $8 \,cm$ due to capillary action. If this experiment is conducted in a freely falling elevator,the length of the water column becomes ....... $cm$.

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 $1.0 \times 10^{3} \;kg m^{-3}$ $(g = 9.8 \;m s^{-2})$.