In to a vessel containing pure water a clean glass tube of radius $3.6 \times 10^{-4} \mathrm{~m}$ is held vertically with 12 cm of the tube above the water level. Now the capillary tube is moved down in to the water so that only 2 cm of its length is above the water surface. Angle of contact $\Theta$ at this position is (given surface tension of water $=7.2 \times 10^{-2} \mathrm{Nm}^{-1}$ and $g=10 \mathrm{~ms}^{-2}$ )

Water from a tap emerges vertically downwards with an initial speed of $1.0 \mathrm{~ms}^{-1}$. The cross-sectional area of the tap is $1 \mathrm{~cm}^2$. Assume that the pressure is constant throughout the stream of water and that the flow is steady. The cross-sectional area of the stream 15 cm below the tap is $\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$

A wind mill converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. The electrical power output P is related to the velocity of wind v as

A cylindrical tank 0.5 m in radius, rests on a platform 1.5 m high. Initially the tank is filled with water to a height of 2.5 m . A small plug whose area is $10^{-4} \mathrm{~m}^2$ is removed from an orifice located on the side of the tank at the bottom. The speed with which the water strikes the ground is: [Assume $g=10 \mathrm{~ms}^{-2}$ ]