JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Fluid Mechanics

A mercury drop of radius

1 0^{- 3} m

is broken into 125 equal size droplets. Surface tension of mercury is

0.45 Nm^{- 1}

. The gain in surface energy is:

(A) $2.26 \times 1 0^{- 5} J$ ✓ Correct
(B) $28 \times 1 0^{- 5} J$
(C) $17.5 \times 1 0^{- 5} J$
(D) $5 \times 1 0^{- 5} J$

Answer: (A)

Solution

Volume is conserved when the drop fragments, so

\frac{4}{3} π R^{3} = 125 \cdot \frac{4}{3} π r^{3}

, giving

r = \frac{R}{5}

. Surface energy equals the surface tension times the area, so the gain is

Δ E = T (125 \cdot 4 π r^{2} - 4 π R^{2}) = 4 π T R^{2} (\frac{125}{25} - 1) = 16 π T R^{2} .

With

T = 0.45 N m^{- 1}

and

R = 1 0^{- 3} m

Δ E = 16 π (0.45) (1 0^{- 3})^{2} = 2.26 \times 1 0^{- 5} J .

JEE Main · 2023 · 01 Feb 2023 · Shift 1 · 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 →