A large tank filled water to a height $h$ is to be emptied through a small hole at the bottom. The ratio of the time taken for the level to fall from $h$ to $\frac{h}{2}$ and that taken for the level to fall from $\frac{h}{2}$ to 0 is

Depth of a river is 100 m magnitude of compressibility of the water is $05 \times 10^{-9} \mathrm{~N}^{-1} \mathrm{~m}^2$. The fractional compression in water at the bottom of the river is (acceleration due to gravity $=10 \mathrm{~m} / \mathrm{s}^2$ )

Two mercury drops, each with same radius $r$ merged to form a bigger drop. $T$ is the surface tension of single drop, then the surface energy of bigger drop is given by

The radius of cross-section of the cylindrical tube of a spray pump is 2 cm . One end of the pump has 50 fine holes each of radius 0.4 mm . If the speed of flow of the liquid inside the tube is $0.04 \mathrm{~ms}^{-2}$. The speed of ejection of the liquid from the holes is