The surface tension of liquid is 0.5 N/m. If a film is held on a ring of area 0.02 ${\mathrm{m}}^2$, its surface energy is

1. $5\times {10}^{-2} \mathrm{joule}$                         

2. $2\times {10}^{-2} \mathrm{joule}$

3. $4\times {10}^{-4} \mathrm{joule}$                         

4. $0.8\times {10}^{-1} \mathrm{joule}$

A film of water is formed between two straight parallel wires of length 10cm each separated by 0.5 cm. If their separation is increased by 1 mm while still maintaining their parallelism, how much work will have to be done (Surface tension of water =$7.2\times {10}^{-2} \mathrm{N}/\mathrm{m}$)

1. $7.22\times {10}^{-6} \mathrm{Joule}$                         

2. $1.44\times {10}^{-5} \mathrm{Joule}$

3. $2.88\times {10}^{-5} \mathrm{Joule}$                         

4. $5.76\times {10}^{-5} \mathrm{Joule}$

A drop of mercury of radius 2 mm is split into 8 identical droplets. Find the increase in surface energy. (Surface tension of mercury is $0.465 \mathrm{J}/{\mathrm{m}}^2$) 

1. $23.4 \mathrm{\mu J}$                             

2. $18.5 \mathrm{\mu J}$

3. $26.8 \mathrm{\mu J}$                              

4. $16.8 \mathrm{\mu J}$

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

1. $1:2^{1/3}$                          2. $2^{1/3} :1$

3. 2:1                              4. 1:2

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

1. H                                 

2. 2H

3. 7H                               

4. 8H

If pressure at half the depth of a lake is equal to 2/3^rd the pressure at the bottom of the lake, then the depth of the lake is:

A spherical drop of water has a radius of 1 mm. If the surface tension of water is $70\times {10}^{-3}$ N/m, the difference in pressures inside and outside the spherical drop is:

In a capillary tube, pressure below the curved surface of the water will be:

Two bubbles A and B are joined through a narrow tube where bubble A is bigger. Then 

1. The size of A will increase

2. The size of B will increase

3. The size of B will increase until the pressure equals

4. None of these

Two soap bubbles have different radii but their surface tension is the same. Mark the correct statement

1. Internal pressure of the smaller bubble is higher than the internal pressure of the larger bubble

2. Pressure of the larger bubble is higher than the smaller bubble

3. Both bubbles have the same internal pressure

4. None of the above