Two cylindrical vessels $A$ and $B$ of different areas of cross-section kept on same horizontal plane are filled with water to the same height. If the volume of water in vessel $A$ is 3 times the volume of water in vessel $B$, then the ratio of the pressures at the bottom of the vessels $A$ and $B$ is

A spherical ball of radius $1 \times 10^{-4} \mathrm{~m}$ and of density $10^4 \mathrm{kgm}^{-3}$ falls freely under gravity through a distance $h$ before entering a tank of water. After entering water if the velocity of the ball does not change, then $h$ is (The coefficient of viscosity of water $9.8 \times 10^{-6} \mathrm{Nsm}^{-2}$ )

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