Let $R_1, R_2$ and $R_3$ be the radii of three mercury drops. A big mercury drop is formed from them under isothermal conditions. The radius of the resultant drop is

A horizontal pipeline carries water in a streamline flow. At a point along the pipe, where the cross-sectional area is $10 \mathrm{~cm}^2$, the velocity of water is $1 \mathrm{~m} / \mathrm{s}$ and pressure is 2000 Pa . The pressure of water at another point where the cross-sectional area $5 \mathrm{~cm}^2$ is

[Given $\rightarrow$ density of water $=1000 \mathrm{~kg} / \mathrm{m}^3$ ]

The amount of work done in blowing a soap bubble such that its diameter increases from 'd' to ' $D$ ' is ( $T=$ surface tension of solution)

When one end of a capillary tube is dipped in water, the height of water column is ' $h$ '. The upward force of 105 dyne due to surface tension is balanced by the force due to the weight of water column. The inner circumference of the capillary tube is

(Surface tension of water $=7 \times 10^{-2} \mathrm{~N} / \mathrm{m}$ )