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 $=10 \mathrm{~ms}^{-2}$ )

When a large bubble rises from the bottom of a lake to the surface, the volume of the bubble becomes 5 times its volume at the bottom of the lake. If $H$ is the atmospheric pressure expressed in terms of water column height, then the depth of the lake is

(The temperature of the water in the lake is same at all points)