The rate of flow of liquid in a tube of radius r, length l, whose ends are maintained at a pressure difference P is $\mathrm{V}=\frac{{\mathrm{\pi QPr}}^4}{\mathrm{\eta l}}$ where $\mathrm{\eta }$ is coefficient of the viscosity and Q is-

Water flows in a streamlined manner through a capillary tube of radius a, the pressure difference being P and the rate of flow Q. If the radius is reduced to a/2 and the pressure increased to 2P, the rate of flow becomes

Water is flowing in a pipe of diameter 4 cm with a velocity 3 m/s. The water then enters into a tube of diameter 2 cm. The velocity of water in the other pipe is

What is the velocity v of a metallic ball of radius r falling in a tank of liquid at the instant when its acceleration is one-half that of a freely falling body ? (The densities of metal and of liquid are $\mathrm{\rho }$ and $\mathrm{\sigma }$ respectively, and the viscosity of the liquid is $\mathrm{\eta }$).

An incompressible fluid flows steadily through a cylindrical pipe which has a radius 2r at point A and a radius r at B further along the flow direction. If the velocity at point A is v, its velocity at point B is:

A homogeneous solid cylinder of length L(L<H/2) . Cross-sectional area A/5 is immersed such that it floats with its axis vertical at the liquid-liquid interface with length L/4 in the denser liquid as shown in the figure. The lower density liquid is open to atmosphere having pressure ${\mathrm{P}}_0$. Then density D of solid is given by

 A wooden block with a coin placed on its top, floats in water as shown in fig. The distance l and h are shown there. After some time the coin falls into the water. Then:
                      

A block of ice floats on a liquid of density 1.2 $g/c{m}^3$ in a beaker. Then level of liquid when ice completely melts-

A vessel of area of cross-section A has liquid to a height H. There is a hole at the bottom of vessel having area of cross-section a. The time taken to decrease the level from ${\mathrm{H}}_1$ to ${\mathrm{H}}_2$ will be

A lead shot of 1mm diameter falls through a long column of glycerine. The variation of its velocity v with distance covered is represented by

Water flows through a frictionless duct with a cross-section varying as shown in fig. Pressure p at points along the axis is represented by

A metallic sphere weighing 3 kg in air is held by a string so as to be completely immersed in a liquid of relative density 0.8. The relative density of metallic is 10. The tension in the string is

From amongst the following curves, which one shows the variation of the velocity v with time t for a small sized spherical body falling vertically in a long column of a viscous liquid -

A liquid does not wet the sides of a solid if the angle of contact is

The meniscus of mercury in the capillary tube is

At which of the following temperatures, the value of surface tension of water is minimum ?

If a glass rod is dipped in mercury and withdrawn out, the mercury does not wet the rod because 

Mercury does not wet glass, wood or iron because

Surface tension of a liquid is found to be influenced by

When a drop of water is dropped on oil surface, then

Small liquid drops assume spherical shape because

It is easy to wash clothes in hot water because its

The force required to separate two glass plates of area ${10}^{-2}{\mathrm{m}}^2$ with a film of water 0.05 mm thick between them, is (Surface tension of water is $70\times {10}^{-3 }$N/m)

Oil spreads over the surface of water whereas water does not spread over the surface of the oil, due to

Cohesive force is experienced between 

The property utilized in the manufacture of lead shots is

The dimensions of surface tension are

A wooden stick 2 m long is floating on the surface of the water. The surface tension of water is 0.07 N/m. By putting soap solution on one side of the stick, the surface tension is reduced to 0.06 N/m. The net force on the stick due to surface tension will be:

Surface tension may be defined as 

The energy needed to break a drop of radius R into n drops of radii r is given by: