What is the velocity $v$ of a metallic ball of radius $r$ falling in a tank of liquid at the instant when its acceleration is one-half that of a freely falling body? (The densities of metal and of liquid are $\rho$ and $\sigma$ respectively, and the viscosity of the liquid is $\eta$ ).

Water is filled up to a height $h$ in a beaker of radius $R$ as shown in the figure. The density of water is $\rho$, the surface tension of water is $T$ and the atmospheric pressure is $p_o$. Consider a vertical section $ABCD$ of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude

Assertion: If work done in increasing the size of a soap film from $10\mathrm{cm}\times 4\mathrm{cm}$ to $10\mathrm{cm}\times 8\mathrm{cm}$ is $2\times {10}^{-4}\mathrm{J},$ then the surface tension is $5\times {10}^{-4}{\mathrm{Nm}}^{-1}$.
Reason:$\mathrm{Work} \mathrm{done}= \mathrm{Surface} \mathrm{tension}\times \mathrm{increase} \mathrm{in} \mathrm{area}$ .

A thread is tied slightly loose to a wire frame as in the figure and the frame is dipped into a soap solution and taken out. The frame is completely covered with the film. When the portion $A$ is punctured with a pin, the thread

In a capillary tube having area of cross-section $"A"$, water rises to a height $\text{'}h\text{'}$. If cross sectional area is reduced to $\frac{\text{'}A\text{'}}{9},$ the rise of water in the capillary tube is

Three liquids of densities ${\rho }_1, {\rho }_2$ and ${\rho }_3$ (with $\left.{\rho }_1>{\rho }_2>{\rho }_3\right),$ having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact ${\theta }_1$ ${\theta }_2$ and ${\theta }_3$ obey 

A capillary tube of radius $r$ is immersed in water and water rises in it to a height $h$. The mass of water in the capillary tube is $5\mathrm{g}$. Another capillary tube of radius $2r$ is immersed in water. The mass of water that will rise in this tube is