A submarine experiences a pressure of $5.05 \times 10^{6} \mathrm{~Pa}$ at a depth of $\mathrm{d}_{1}$ in a sea. When it goes further to a depth of $d_{2}$, it experiences a pressure of $8.08 \times 10^{6} \mathrm{~Pa}$. Then $d_{2}-d_{1}$ is approximately (density of water $=10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ and acceleration due to gravity $=10 \mathrm{~ms}^{-2}$)

JEE Main · 2019 · 10 Apr 2019 · Shift 2 · Fluid Mechanics

A submarine experiences a pressure of

5.05 \times 1 0^{6} Pa

at a depth of

d_{1}

in a sea. When it goes further to a depth of

d_{2}

, it experiences a pressure of

8.08 \times 1 0^{6} Pa

. Then

d_{2} - d_{1}

is approximately (density of water

= 1 0^{3} kg / m^{3}

and acceleration due to gravity

= 10 ms^{- 2}

)

(A)400 m
(B)500 m
(C)600 m
(D)300 m✓ Correct

Answer: (D)

Solution

The pressure at depth grows as

ρ g d

, so the gap between the two readings is

Δ P = 8.08 \times 1 0^{6} - 5.05 \times 1 0^{6} = 3.03 \times 1 0^{6} Pa

. Converting this to a depth difference,

d_{2} - d_{1} = \frac{Δ P}{ρ g} = \frac{3.03 \times 1 0 ^{6}}{1 0 ^{3} \times 10} \approx 300 m

JEE Main · 2019 · 10 Apr 2019 · 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 →