If the excess pressures inside two soap bubbles are in the ratio $2: 3$, then the ratio of the volumes of the somp bubbles is

The velocities of air above and below the surfaces of a flying aeroplane wing are $50 \mathrm{~ms}^{-1}$ and $40 \mathrm{~ms}^{-1}$, respectively. If the area of the wing is $10 \mathrm{~m}^{2}$ and the mass of the aeroplane is 500 kg , then as time passes of (density of air $=13 \mathrm{~kg} \mathrm{~m}^{-3}$ )

Three identical vessels are filled up to the same height with three different liquids $A, B$ and $C$ of densities $\rho_{A} \rho_{B}$ and $\rho_{C}$, respectively. If $\rho_{A} > \rho_{B} > \rho_{C}$, then the pressure at the bottom of the vessels is

A wooden cube of side 10 cm floats at the interface between water and oil with its lower surface 3 cm below the interface. If the density of oil is $0.9 \mathrm{~g} \mathrm{~cm}^{-3}$, the mass of the wooden cube is

The excess pressure inside a soap bubble of radius 0.5 cm is balanced by the pressure due to an oil column of height 4 mm . If the density of the oil is $900 \mathrm{~kg} \mathrm{~m}^{-3}$, then the surface tension of the soap solution is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

Water flows through a horizontal pipe of variable cross-section at the rate of $12 \pi$ litre per minute. The velocity of the water at the point, where the diameter of the pipe becomes 2 cm is

The height of water level in a tank of uniform cross-section is 5 m . The volume of the water leaked in 5 s through a hole of area $2.4 \mathrm{~mm}^2$ miade at the bottom of the tank is (Assume the level of the water in the tank remains constant and acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

A straw of circular cross-section of radius $R$ and negligible thickness is dipped vertically into a liquid of surface tension $T$. If the contact angle between the liquid and the straw material is $53^{\circ}$. The force acting on the straw due to surface tension of the liquid is $\left(\cos 53^{\circ}=0.6\right)$

A solid metal sphere released in a vertical liquid column has attained terminal velocity in the downward direction. The magnitudes of viscous force, buoyant force and gravitational force acting on it are $F_V, F_B$ and $F_W$ respectively. Then, the correct relation between them is