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

Two narrow bores of diameter $5.0 \, mm$ and $8.0 \, mm$ are joined together to form a $U$-shaped tube open at both ends. If this $U$-tube contains water,what is the difference in the level of two limbs of the tube? [Take surface tension of water $T = 7.3 \times 10^{-2} \, Nm^{-1}$,angle of contact $= 0$,$g = 10 \, ms^{-2}$ and density of water $\rho = 1.0 \times 10^{3} \, kg \, m^{-3}$] (in $mm$)

Two tubes of same length and diameters $4 \ mm$ and $8 \ mm$ are joined together to form a $U$-shaped tube open at both the ends. If the $U$-tube contains water,then the difference between the levels of water in the two limbs of the tube is (Surface tension of water at the temperature of experiment is $7.3 \times 10^{-2} \ N \ m^{-1}$,angle of contact $= 0^{\circ}$,density of water $= 1.0 \times 10^3 \ kg \ m^{-3}$ and acceleration due to gravity $= 10 \ m \ s^{-2}$) (in $mm$)

Water rises up to a height $h$ in a capillary tube on the surface of the Earth in a stationary condition. The value of $h$ increases if this tube is taken:

$A$ 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 is $5 \, g$. Another capillary tube of radius $2r$ is immersed in water. The mass of water that will rise in this tube is $........ \, g$.

Water rises in a capillary tube of radius $r$ up to a height $h$. The mass of water in the capillary is $m$. The mass of water that will rise in a capillary tube of radius $\frac{r}{3}$ will be: