What is the terminal velocity of a rain drop of radius 0.02 mm ?
[Note that the coefficient of viscosity of air is $1.8 \times 10^{-5} \mathrm{N} / \mathrm{m}^2$, density of water is $1000 \mathrm{~kg} / \mathrm{m}^3$. Use, $g=10 \mathrm{~m} / \mathrm{s}^2$ and density of air can be neglected in comparision with density of water]
A large storage tank, open to the atmosphere at top and filled with water, develops a small hole in its side at a point 20.0 m below the water level. If the rate of flow from the hole is $3.08 \times 10^{-5} \mathrm{~m}^3 / \mathrm{s}$, then the diameter of the hole is (take, $g=10 \mathrm{~m} / \mathrm{s}^2$ )
An air bubble of radius 1 mm is at a depth of 8 cm below the free surface of a liquid column. If the surface tension and density of the liquid is $0.1 \mathrm{~N} / \mathrm{m}$ and 2000 $\mathrm{kg} / \mathrm{m}^3$, respectively, by what amount is the pressure inside the bubble greater than the atmospheric pressure? (take, $g=10 \mathrm{~m} / \mathrm{s}^2$ )
A hydraulic lift as shown in the figure is used to lift a mass of 1000 kg , which is placed on a piston $\left(P_1\right)$ of area $1 \mathrm{~m}^2$. If the cross-section area of the piston $\left(P_2\right)$ at the other end is $0.01 \mathrm{~m}^2$, then how much mass needs to be put on it to lift the 1000 kg ?

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