The radius of a soap bubble is r. The surface tension of soap solution is 'S'. Keeping temperature constant, the radius of the soap bubble is soubled. The energy necessary for this will be

1. $24<mspace\; width="1em"></mspace>{\mathrm{\pi r}}^2\mathrm{S}$

2. $8<mspace\; width="1em"></mspace>{\mathrm{\pi r}}^2\mathrm{S}$

3. $16<mspace\; width="1em"></mspace>{\mathrm{\pi r}}^2\mathrm{S}$

4. $12<mspace\; width="1em"></mspace>{\mathrm{\pi r}}^2\mathrm{S}$

The surface tension of a liquid is 5 N/m. If a film is held on a ring of area 0.02 m², its surface energy is about

1. $5\times {10}^{-2}<mspace\; width="1em"></mspace>\mathrm{J}$

2. $2.5\times {10}^{-2}<mspace\; width="1em"></mspace>\mathrm{J}$

3. $2\times {10}^{-1}<mspace\; width="1em"></mspace>\mathrm{J}$

4. $3\times {10}^{-1}<mspace\; width="1em"></mspace>\mathrm{J}$

Two soap bubbles having radii 3 cm and 4 cm in vacuum, coalesce under isothermal conditions. The radius of the new bubble is

1. 1 cm

2. 5 cm

3. 7 cm

4. 3.5 cm

The work done to break a spherical drop of radius R in n drops of equal size is proportional to

1. $\frac{1}{{\mathrm{n}}^{2/3}}-1$

2. $\frac{1}{{\mathrm{n}}^{1/3}}-1$

3. ${\mathrm{n}}^{1/3}-1$

4. ${\mathrm{n}}^{4/3}-1$

The kerosene oil rises up in the wick of a lamp

1. Due to high surface tension of coil

2. Because the wick attracts the oil

3. Because the wick decreases the surface tension of oil

4. Due to capillaries formed in the wick

Ploughing help to retain water by soil

1. By creating capillaries

2. By breaking capillaries 

3. By turning the soil upside down

4. None of these

A capillary tube of radius r is immersed in a liquid and mass of liquid, which rises up in it is M. If the radius of tube is doubled, then the mass of liquid which will rise in capillary tube will be

1. 2 M

2. M

3. M/M

4. M/4

A massless inextensible string in the form of a loop is placed on a horizontal film of soap solution of surface tension T. If film is pierced inside the loop and it converts into a circular loop of diameter d, then the tension produced in the string is

1. Td

2. $\mathrm{\pi Td}$

3. ${\mathrm{\pi d}}^2\mathrm{T}$

4. $\frac{{\mathrm{\pi d}}^2\mathrm{T}}{4}$

A tank is filled with water to a height H. A hole is made in one of the walls at a depht D below the water surface. The distance x from the foot of the wall at which the stream of water coming out the tank strikes the ground is given by

1. $\mathrm{x}=2{\left[\mathrm{D}\right(\mathrm{H}-\mathrm{D}\left)\right]}^{1/2}$

2. $\mathrm{x}=2{\left(\mathrm{gD}\right)}^{1/2}$

3. $\mathrm{x}=2{\left[\mathrm{D}\right(\mathrm{H}+\mathrm{D}\left)\right]}^{1/2}$

4. None of these

In streamline flow of liquid, the total energy of liquid is constant at:

1. all points

2. inner points

3. outer points

4. none of the above