Question

A submarine experiences pressure \[5.05 \times {10^6}Pa\] at a depth of ${d_1}$ in a sea. When it goes further to a depth of ${d_2}$ , it experiences a pressure of \[8.08 \times {10^6}Pa\] , then ${d_2} - {d_1}$ is approximate. (Density of water $ = {10^3}kg/{m^3}$ and acceleration due to gravity \[ = 10m{s^{ - 2}}\] )
$\left( a \right)$ $500m$
$\left( b \right)$ $400m$
$\left( c \right)$ $300m$
$\left( d \right)$ $600m$

Answer 1

Hint Here in this question the pressure experienced by the submarine at the different depth has been given and we have to find out the change in the density for which the water density is also given. We will apply the pressure formula and will solve it to get the result.
Formula:
The pressure experienced will be equal to
${\rho _0} + \rho g{d_1} = {P_1}$
Where,
${\rho _0}$ , will be the atmospheric pressure and $\rho $ will be the density and the $g$ will be the acceleration due to gravity and the ${P_1}$ will be the experienced pressure.

Complete Step By Step Solution So first of all we will see what are known terms we have and then we will find the required result.
So according to the question, we have
\[{P_1} = 5.05 \times {10^6}Pa\]And
\[{P_2} = 8.08 \times {10^6}Pa\]
$\rho = {10^3}kg/{m^3}$
So we have these values given, now we will write the equation.
For the distance ${d_1}$ ,
${\rho _0} + \rho g{d_1} = {P_1}$
For the distance ${d_2}$ ,
${\rho _0} + \rho g{d_2} = {P_2}$
So now we will subtract the second equation to the first equation, we get
$ \Rightarrow \rho g\left( {{d_2} - {d_1}} \right) = {P_2} - {P_1}$
Now after putting the values, we will get the following
$ \Rightarrow {10^3}kg/{m^3} \times 10\left( {{d_2} - {d_1}} \right) = 8.08 \times {10^6}Pa - 5.05 \times {10^6}Pa$
Now after solving the above equation we will get,
$ \Rightarrow {d_2} - {d_1} = 303m$
So since the third option is close to our answer, we can say that the correct choice will be an option $c$

Therefore the approximate distance between the two depths will be equal to the $300m$.

Note Density is the mass of a substance per unit volume.
All substances are made of matter i.e. molecules and atoms. So the total mass of such atoms or molecules in a fixed volume of various substances will differ based on Whether the atoms are loosely arranged, or compactly arranged, near or far apart (solids are compact, liquids and gas molecules are moving) The molecular weight of the atoms and molecules (weight of protons + neutrons) Temperature of the substance (molecular space is more in higher temp)