Question:
The density of water at the surface of the ocean is $\rho$ and atmospheric pressure is $p _{0}$. If the bulk modulus of water is $K$, what is the density of ocean water at a depth where the pressure is $n p_{0}$ ?
The density of water at the surface of the ocean is $\rho$ and atmospheric pressure is $p _{0}$. If the bulk modulus of water is $K$, what is the density of ocean water at a depth where the pressure is $n p_{0}$ ?
Updated On: Jul 7, 2022
- $\frac{\rho k}{k-n p_{0}}$
- $\frac{\rho k}{k+n p_{0}}$
- $\frac{\rho k}{k-\left(n-1\right)p_{0}}$
- $\frac{\rho k}{k+\left(n-1\right)p_{0}}$
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The Correct Option is C
Solution and Explanation
Variation of density with pressure is given by
$\rho'$$=\frac{\rho}{\left[1-\frac{\Delta p}{k}\right]}$
Here, $\Delta p$ $=np_{0}-p_{0}$ $=\left(n-1\right)p_{0}$
$\therefore\quad$ $\rho'$ $=\frac{\rho}{1-\frac{\left(n-1\right)p_{0}}{k}}$ $=\frac{\rho k}{k-\left(n-1\right)p_{0}}$
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Concepts Used:
Pressure
Pressure is defined as the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
Everyday examples of pressure are:
- The working of the vacuum cleaner is an example of pressure. The fan inside the vacuum creates a low-pressure region which makes it easy to suck the dust particles inside the vacuum.
- Using a knife for cutting is another example of pressure. The area exposed from the knife is small but the pressure is high enough to cut the vegetables and fruits.
Formula:
When a force of ‘F’ Newton is applied perpendicularly to a surface area ‘A’, then the pressure exerted on the surface by the force is equal to the ratio of F to A. The formula for pressure (P) is:
P = F / A
Units of Pressure:
The SI unit of pressure is the pascal (Pa)
A pascal can be defined as a force of one newton applied over a surface area of a one-meter square.