JEE Main · 2021 · 20 Jul 2021 · Shift 2 · Fluid Mechanics

WhatsApp Email

Two small drops of mercury each of radius R coalesce to from a single large drop. The ratio of total surface energy before and after the change is :

(A) $2^{\frac{1}{3}} : 1$ ✓ Correct
(B) $1 : 2^{\frac{1}{3}}$
(C) $2 : 1$
(D) $1 : 2$

Answer: (A)

Solution

Volume is conserved when the drops merge, so

2 \times \frac{4}{3} π R^{3} = \frac{4}{3} π R^{'3}

and

R^{'} = 2^{1/3} R

. Surface energy is the surface tension times the area, so the energy before the merger is

σ \times 2 \times 4 π R^{2} = 8 π σ R^{2}

and after it is

σ \times 4 π R^{'2} = 4 π σ 2^{2/3} R^{2}

. The ratio is

\frac{8 π σ R ^{2}}{4 π σ 2 ^{2/3} R ^{2}} = \frac{2}{2 ^{2/3}} = 2^{1/3}

so the total surface energy before and after the change is in the ratio

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

JEE Main · 2021 · 20 Jul 2021 · Shift 2 · Single correct option

Practise more: all JEE Main PYQs on Fluid Mechanics →

More JEE Main questions on Fluid Mechanics

Given below are two statements:
Statement I: Pressure of fluid is exerted only on a solid surface in contact as the fluid-pressure does not exist everywhere in a still fluid.
Statement II: Excess potential energy of the molecules on the surface of a liquid, when compared to inter …
JEE Main 2026View solution →
When a part of a straight capillary tube is placed vertically in a liquid, the liquid raises upto certain height h. If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by $1%$ each, then the height of the liquid in the tube …
JEE Main 2026View solution →
Surface tension of two liquids (having same densities), $T_{1}$ and $T_{2}$ , are measured using capillary rise method utilizing two tubes with inner radii of $r_{1}$ and $r_{2}$ where $r_{1} > r_{2}$ . The measured liquid heights in these tubes are …
JEE Main 2026View solution →
The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is $20 cm / s$ . The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be
____ $cm / s$ .
JEE Main 2026View solution →
A small metallic sphere of diameter 2 mm and density $10.5$ g/cm³ is dropped in glycerine having viscosity 10 Poise and density $1.5$ g/cm³ respectively. The terminal velocity attained by the sphere is $____$ cm/s.
( $π = \frac{22}{7}$ and $g = 10$ m/s²)
JEE Main 2026View solution →
Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of $10 cm / s$ coalesce to form a bigger drop. The terminal velocity of bigger drop is ______ $cm / s$ .
JEE Main 2026View solution →