Properties of Matter 2 Question 1

1. A submarine experience a pressure of 5.05×106Pa at a depth of d1 in a sea. When it goes further to a depth of d2, it experiences a pressure of 8.08×106Pa, then d2d1 is approximately (density of water =103kg/m3 and acceleration due to gravity =10ms2 ) (2019 Main, 10Apr II)

(a) 500m

(b) 400m

(c) 600m

(d) 300m

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Answer:

Correct Answer: 1. (d)

Solution:

  1. Pressure inside a fluid volume open to atmosphere is

p=p0+hρg

where, p= pressure at depth h,h=depth,

ρ= density of fluid 

and g= acceleration due to gravity.

In problem given,

when h=d1, pressure p1=5.05×106Pa and when h=d2, pressure p2=8.08×106Pa

So, we have

p1=p0+d1ρg=5.05×106 and p2=p0+d2ρg=8.08×106p2p1=(d2d1)ρg=3.03×106d2d1=3.03×106ρg

Given, ρ=103kgm3

and g=10ms2

d2d1=3.03×106103×10

=303m300m



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