Fluid Mechanics

In a capillary tube having area of cross-section A, water rises to a height 'h'. If cross-sectional area is reduced to \(\frac{A}{9}\), the rise of water in the capillary tube is

Under isothermal conditions, two soap bubbles of radii '\(r_1\)' and '\(r_2\)' combine to form a single soap bubble of radius '\(R\)'. The surface tension of soap solution is ( \(P=\) outside pressure)

The force required to take away a flat circular plate of radius \(2 \mathrm{~cm}\) from the surface of water is \(\left[\right.\)Surface tension of water \(\left.=70 \times 10^{-3} \mathrm{Nm}^{-1}, \pi=\frac{22}{7}\right]\)

Let '\(\mathrm{R_1}\)' and '\(\mathrm{R_2}\)' are radii of two mercury drops. A big mercury drop is formed from them under isothermal conditions. The radius of the resultant drop is

Air is pushed in a soap bubble to increase its radius from 'R' to '2R'. In this case, the pressure inside the bubble

The surface energy of a liquid drop is 'U'. It splits up into 512 equal droplets. The surface energy becomes

A body of density \(V\) is dropped from (at rest) height '\(h\)' into a lake of density '\(\delta\)' \((\delta > \rho)\). The maximum depth to which the body sinks before returning to float on the surface is [Neglect all dissipative forces]

What should be the radius of water drop so that excess pressure inside it is 72 Nm\(^{-2}\) ? (The surface tension of water 7.2 \(\times\) 10\(^{-2}\) Nm\(^{-1}\))

If the surface tension of a soap solution is $3 \times 10^{-2} \mathrm{~N} / \mathrm{m}$ then the work done in forming a soap film of $20 \mathrm{~cm} \times 5 \mathrm{~cm}$ will be

Water rises upto a height $h$ in a capillary tube on the surface of the earth. The value of $h$ will increase, if the experimental setup is kept in [ $g=$ acceleration due to gravity]

Two spherical rain drops reach the surface of the earth with terminal velocities having ratio $16: 9$. The ratio of their surface area is

Two small drops of mercury each of radius \(r\) coalesce to form a large single drop. The ratio of the total surface energies before and after the change is

A small metal sphere of mass \(M\) and density \(d_1\) when dropped in a jar filled with liquid moves with terminal velocity after sometime. The viscous force acting on the sphere is (\(d_2=\) density of liquid and \(g=\) gravitational acce...

Water rises in a capillary tube of radius \(r\) upto a height \(h\). The mass of water in a capillary is \(m\). The mass of water that will rise in a capillary of radius \(\frac{r}{4}\) will be

The work done in blowing a soap bubble of radius \(R\) is \(W\). The work done in blowing a bubble of radius \(2 R\) of the same soap solution is

A large open tank containing water has two holes to its wall. A square hole of side $a$ is made at a depth \(y\) and a circular hole of radius \(r\) is made at a depth \(16 y\) from the surface of water. If equal amount of water comes out t...

A square frame of each side \(L\) is dipped in a soap solution and taken out. The force acting on the film formed is (\(T=\) surface tension of soap solution)

A molecule of water on the surface experiences a net

When a large bubble rises from bottom of a water lake to its surface, then its radius doubles. If the atmospheric pressure is equal to the pressure of height $H$ of a certain water column, then the depth of lake will be

Eight identical drops of water falling through air with uniform velocity of $10 \mathrm{~cm} / \mathrm{s}$ combine to form a single drop of big size, then terminal velocity of the big drop will be

A metal sphere of radius ' $R$ ' and density ' $\rho_1$ ' is dropped in a liquid of density ' $\sigma$ ' moves with terminal velocity ' $v$ '. Another metal sphere of same radius and density ' $\rho_2$ ' is dropped in the same liquid, its t...

Two capillary tubes of different diameters are dipped in water. The rise of water is

Two small drops of mercury each of radius ' $R$ ' coalesce to form a large single drop. The ratio of the total surface energies before and after the change is

In air, a charged soap bubble of radius ' $R$ ' breaks into 27 small soap bubbles of equal radius ' $r$ '. Then the ratio of mechanical force acting per unit area of big soap bubble to that of a small soap bubble is

Two light balls are suspended as shown in figure. When a stream of air passes through the space between them, the distance between the balls will

The excess of pressure, due to surface tension, on a spherical liquid drop of radius ' $R$ ' is proportional to

Which one of the following statement is correct?