Work done in splitting a drop of water of 1 mm radius into ${10}^6$ droplets is (Surface tension of water $=72\times {10}^{-3} \mathrm{J}/{\mathrm{m}}^2$)

(1) $9.58\times {10}^{-5} \mathrm{J}$                 

(2) $8.95\times {10}^{-5} \mathrm{J}$

(3) $5.89\times {10}^{-5} \mathrm{J}$                   

(4) $5.98\times {10}^{-5} \mathrm{J}$

The amount of work done in blowing a soap bubble such that its diameter increases from d to D is (T= surface tension of the solution)

1. $4\mathrm{\pi }({\mathrm{D}}^2-{\mathrm{d}}^2)\mathrm{T}$                     

2. $8\mathrm{\pi }({\mathrm{D}}^2-{\mathrm{d}}^2)\mathrm{T}$

3. $\mathrm{\pi }({\mathrm{D}}^2-{\mathrm{d}}^2)\mathrm{T}$                       

4. $2\mathrm{\pi }({\mathrm{D}}^2-{\mathrm{d}}^2)\mathrm{T}$

A spherical drop of oil of radius 1 cm is broken into 1000 droplets of equal radii. If the surface tension of oil is 50 dynes/cm, the work done is 

(1) 18 $\pi$ ergs                     

(2) 180 $\pi$ ergs

(3) 1800 $\pi$ ergs                 

(4) 8000 $\pi$ ergs

If the surface tension of a liquid is T, the gain in surface energy for an increase in liquid surface by A is

(1) ${\mathrm{AT}}^{-1}$                       

(2) $\mathrm{AT}$

(3) ${\mathrm{A}}^2\mathrm{T}$                         

(4) ${\mathrm{A}}^2{\mathrm{T}}^2$

The surface tension of a liquid at its boiling point

(1) Becomes zero

(2) Becomes infinity

(3) is equal to the value at room temperature

(4) is half to the value at the room temperature

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

(a) $5\times {10}^{-2} \mathrm{joule}$                         (b) $2\times {10}^{-2} \mathrm{joule}$

(c) $4\times {10}^{-4} \mathrm{joule}$                         (d) $0.8\times {10}^{-1} \mathrm{joule}$

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