Physics Mechanical Properties of Fluids

The amount of energy required to form a bubble of radius $2\mathrm{c}\mathrm{m}$ from a soap solution is nearly: (surface tension of soap solution $=0.03\mathrm{N}{\mathrm{m}}^{-1}$  )

Consider a water tank as shown in the figure. It's cross-sectional area is 0.4 m². The tank has an opening B near the bottom whose cross-sectional area is 1cm². A load of 24 kg is applied on the water at the top when the height of the water level is 40 cm above the bottom, the velocity of water coming out the opening B is v ms^-1.

The value of v, to the nearest integer, is.
[Take value of g to be 10 ms^-2]

When two soap bubbles of radii a and b (b > a) coalesce, the radius of curvature of common surface is:

A cube of metal is subjected to a hydrostatic pressure 4GPa. The percentage change in the length of the side of the cube is close to: (Given bulk modulus of metal, B = 8 * 10¹⁰ Pa)

A fluid is flowing through a horizontal pipe of varying cross-section, with speed v ms⁻¹ at a point where the pressure is P Pascal. At another point where pressure is P/2 Pascal its speed is V ms⁻¹. If the density of the fluid is ρ kgm⁻³ and the flow is streamline, then V is equal to:

Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density d. The area of the base of both vessels is S but the height of liquid in one vessel is x1 and in the other, x2. When both cylinders are connected through a pipe of negligible volume very close to the bottom, the liquid flows from one vessel to the other until it comes to equilibrium at a new height. The change in energy of the system in the process is :

A air bubble of radius 1 cm in water has an upward acceleration 9.8 cm s?². The density of water is 1gmcm?³ and water offers negligible drag force on the bubble. The mass of the bubble is: (g = 980 cm/s²).