JEE Main · 2024 · 09 Apr 2024 · Shift 2 · Fluid Mechanics

WhatsApp Email

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is :

(A) $1 : 9$
(B) $1 : 3$
(C) $1 : 81$
(D) $1 : 27$ ✓ Correct

Answer: (D)

Solution

Excess pressure inside a soap bubble is

Δ P = \frac{4 T}{r}

(two surfaces).

Given

Δ P_{1} = 3Δ P_{2}

\frac{4 T}{r _{1}} = 3 \cdot \frac{4 T}{r _{2}} ⟹ r_{2} = 3 r_{1}

Ratio of volumes:

\frac{V _{1}}{V _{2}} = (\frac{r _{1}}{r _{2}})^{3} = (\frac{1}{3})^{3} = \frac{1}{27}

V_{1} : V_{2} = 1 : 27

JEE Main · 2024 · 09 Apr 2024 · 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 →