A liquid drop of diameter D breaks upto into 27 small drops of equal size. If the surface tension of the liquid is $\mathrm{\sigma }$, then change in surface energy is 

(a) ${\mathrm{\pi D}}^2\mathrm{\sigma }$                          (b) $2{\mathrm{\pi D}}^2\mathrm{\sigma }$

(c) $3{\mathrm{\pi D}}^2\mathrm{\sigma }$                         (d) $4{\mathrm{\pi D}}^2\mathrm{\sigma }$

One thousand small water drops of equal radii combine to form a big drop. The ratio of final surface energy to the total initial surface energy is 

1. 1000 : 1               

2. 1 : 1000

3. 10 : 1                   

4. 1 : 10

A big drop of radius R is formed by 1000 small droplets of water, then the radius of small drop is

1. R/2                                     

2. R/5

3. R/6                                     

4. R/10

8000 identical water drops are combined to form a big drop. Then the ratio of the final surface energy to the initial surface energy of all the drops together is 
1. 1 : 10                     

2. 1 : 15

3. 1 : 20                     

4. 1 : 25

When two small bubbles join to form a bigger one, energy is

1. Released

2. Absorbed

3. Both (1) and (2)

4. None of these

A water film is formed between the two straight parallel wires, each of length \(10~\text{cm}\), kept at a separation of \(0.5~\text{cm}.\)Now, the separation between them is increased by \(1~\text{mm}\) without breaking the water film. The work done for this is
(surface tension of water =\(7.2\times 10^{-2}~\text{N/m}\))
1. \(7.22\times 10^{-6}~\text{J}\)
2. \(1.44\times 10^{-5}~\text{J}\)
3. \(2.88\times 10^{-5}~\text{J}\)
4. \(5.76\times 10^{-5}~\text{J}\)

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. $16.8 \mathrm{\mu J}$

If two soap bubbles of equal radii r coalesce then the radius of curvature of interface between two bubbles will be

1. r                                 

2. 0

3. Infinity                         

4. 1/2r

The angle of contact between glass and mercury is

1. 0°

2. 30°

3. 90°

4. 135°

A mercury drop does not spread on a glass plate because the angle of contact between glass and mercury is

1. Acute

2. Obtuse

3. Zero

4. $90°$