A closed water tank has cross-sectional area $$A$$. It has a small hole at a depth of $$h$$ from the free surface of water. The radius of the hole is $$r$$ so that $$r \ll \sqrt{\frac{A}{\pi}}$$. If $$p_o$$ is the pressure inside the tank above water level and $$p_a$$ is the atmospheric pressure, the rate of flow of the water coming out of the hole is ( $$\rho$$ is density of water)

Two capillary tubes $$P$$ and $$Q$$ are dipped vertically in water. The height of water level in capillary tube $$P$$ is $$\frac{2}{3}$$ of the height in capillary tube $$Q$$. The ratio of their diameter is

Iceberg floats in water with part of it submerged. What is the fraction of the volume of iceberg submerged, if the density of ice is $$\rho_i=0.917 \mathrm{~g} \mathrm{~cm}^{-3}$$ ?

A cylindrical container containing water has a small hole at height of $$H=8 \mathrm{~cm}$$ from the bottom and at a depth of $$2 \mathrm{~cm}$$ from the top surface of the liquid. The maximum horizontal distance travelled by the water before it hits the ground $$x$$ is