Two capillaries of the same material but of different radii are dipped in a liquid. In one of the capillaries,the liquid rises to a height of $22 \ cm$ and in the other to $66 \ cm$. The ratio of their radii is

The correct relation for the capillary rise $h$ in a tube of radius $r$ is:

According to Poiseuille's law,the pressure drop per unit length required to overcome viscous forces is $\Delta P = \frac{8 \eta v}{r^2}$,where $r$ is the radius of the cross-section,$v$ is the fluid velocity,and $\eta$ is the coefficient of viscosity. $A$ capillary tube of radius $a$ is dipped in a liquid of density $\rho$,surface tension $T$,and coefficient of viscosity $\eta$. The liquid starts rising in it so that its height $h(t)$ is a function of time $t$. The resulting rate of change of the momentum of the liquid column in the capillary (taking vertically up to be the positive direction and the contact angle to be close to $0^{\circ}$) is $-\pi a^2 \rho gh + F$. Then $F$ is ($g$ is the acceleration due to gravity):

Water rises up to a height $h$ in a capillary tube of a certain diameter. This capillary tube is replaced by a similar tube of half the diameter. Now,the water will rise to a height of:

Why is moisture retained in the soil when a farm is ploughed?

$A$ capillary tube is dipped in water and it is $20 \, cm$ outside water. The water rises up to $8 \, cm$. If the entire arrangement is put in a freely falling elevator,the length of the water column in the capillary tube will be ........ $cm$.