What is the relation obeyed by the angles of contact $$\theta_1, \theta_2$$ and $$\theta_3$$ of 3 liquids of different densities $$P_1, P_2$$ and $$P_3$$ respectively $$(\mathrm{P}_1 < \mathrm{P}_2 < \mathrm{P}_3$$) when they rise to the same capillary height in 3 identical capillaries and having nearly same surface tension $$\mathrm{T}$$ ?

Water flows from a tap with steady flow, through a cross sectional area of $$10^{-3} \mathrm{~m}^2$$ with a speed of $$0.5 \mathrm{~ms}^{-1}$$. Assume the pressure is constant throughout the stream of water. The cross sectional area of the stream $$0.19 \mathrm{~m}$$ below the tap is

Modulus of rigidity of an incompressible liquid is

64 rain drops of the same radius are falling through air with a steady velocity of $$0.5 \mathrm{~cm} \mathrm{~s}^{-1}$$. If the drops coalesce, the terminal velocity would be

A block of wood floats in water with $$(4 / 5)$$ th of its volume submerged. If the same block just floats in a liquid, the density of the liquid is (in $$\mathrm{kgm}^{-3}$$)

A balloon with mass $m$ is descending down with an acceleration $$a$$ (where, $$a < g$$ ). How much mass should be removed from it so that it starts moving up with an acceleration $$a$$ ?

The speeds of air-flow on the upper and lower surfaces of a wing of an aeroplane are $$v_1$$ and $$v_2$$, respectively. If $$A$$ is the cross-sectional area of the wing and $$\rho$$ is the density of air, then the upward lift is

Water from a tap of cross-sectional area $$1 \mathrm{~cm}^2$$, falls vertically downwards at $$2 \mathrm{~m} / \mathrm{s}$$. The cross sectional area of the stream, $$20 \mathrm{~cm}$$ below the tap is (assume that pressure is constant throughout and the flow is streamlined; $$\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$$

A raft of density 600 g/m$$^3$$ and mass 120 kg floats in water. How much weight can be put on the raft to make it just sink?

Water is poured in a tank through a cylindrical tube of area of cross-section A and ejecting water at a constant speed 4 m/s. the tank contains a hole of area $$\frac{A}{2}$$ at bottom. Level of water in the tank will not go up beyond

According to Pascal's law, pressure in a fluid at rest is the same at all points, if

The surface tension of a liquid at its boiling point

A ball floats on the surface of water in a container exposed to the atmosphere. When the container is covered and the air is partially removed, then the ball

A frame made of metallic wire enclosing a surface area A is covered with a soap film. If the area of the frame of metallic wire is reduced by 50%, then the energy of the soap film will be changed by

A fluid is in streamline flow across a horizontal pipe of variable area of cross-section. For this which of the following statements is correct?