Q116 / 150 · MHT CET 2019 (02 May Shift 1) · Physics

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
$2^{\frac{2}{3}} : 1$
B
$\sqrt{2} : 1$
Correct answer
C
$2^{\frac{1}{3}} : 1$
D
$2 : 1$

Solution

Surface enegy

\propto

Surface Area

∵ (\frac{4}{3} π R^{3}) \times 2 = \frac{4}{3} π R_{0}^{3}

\Rightarrow R_{0} = R {(2)}^{\frac{1}{3}}

∴ \frac{{(S u r f a c e E n e r g y)}_{b e f o r e}}{{(S u r f a c e E n e r g y)}_{a f t e r}} = \frac{(4 π R^{2}) \times 2}{4 π R^{2} {(2)}^{\frac{2}{3}}}

= \frac{2^{\frac{1}{3}}}{1}

Hence, the correct answer is option: 'C'.

Relevant Questions

The excess pressure inside a soap bubble of radius cm is dyne/cm . The surface tension of soap solution in dyne /cm is20 Apr, 2026 (M)Surface tension
If erg of work is done in blowing a soap bubble of radius ' ', the additional work required to be done to blow it to a radius equal to is20 Apr, 2026 (M)Surface tension
If we dip capillary tubes of different radii in water and the water rises to different heights in them, then ( .........)20 Apr, 2026 (E)Surface tension
The pressures inside two soap bubbles A and B are atmosphere and atmosphere respectively. The ratio of volume of bubble A to that of bubble 19 Apr, 2026 (M)Surface tension
One large soap bubble of diameter 'D' breaks into bubbles having surface tension 'T'. The change in surface energy is19 Apr, 2026 (M)Surface tension
In most liquids, with rise in temperature surface tension of liquid19 Apr, 2026 (E)Surface tension