On putting a capillary tube in a pot filled with water,the level of water rises up to a height of $4 \,cm$ in the tube. If a tube of half the diameter is used instead,the water will rise to a height of nearly ............. $cm$.

The quantity on which the rise of liquid in a capillary tube does not depend 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):

What is capillarity? Give two practical illustrations of capillarity.

The angle of contact between glass and water is $0^\circ$ and it rises in a capillary up to $6 \text{ cm}$ when its surface tension is $70 \text{ dynes/cm}$. Another liquid of surface tension $140 \text{ dynes/cm}$,angle of contact $60^\circ$ and relative density $2$ will rise in the same capillary by ........ $\text{cm}$.

Water rises in a capillary tube up to a height $h$. If this capillary tube is tilted by an angle of $45^o$,then the length of the water column in the capillary tube becomes