A cube of metal is subjected to a hydrostatic pressure of $4 \,GPa$. The percentage change in the length of the side of the cube is close to (Given bulk modulus of metal, $\left. B =8 \times 10^{10} Pa \right)$
- 0.6
- 1.67
- 5
- 20
The Correct Option is B
Solution and Explanation
\(B =-\frac{\Delta P }{\frac{\Delta V }{ V }}\)
\(\left|\frac{\Delta V }{ V }\right|=\frac{\Delta P }{ B }\) \(=\frac{4 \times 10^{9}}{8 \times 10^{10}}=\frac{1}{20}\)
\(\frac{\Delta \ell}{\ell}=\frac{1}{3} \times \frac{\Delta V }{ V }=\frac{1}{60}\)
Percentage change \(=\frac{\Delta \ell}{\ell} \times 100 \%\) \(=\frac{1}{60}\times100\%=1.67 \%\)
So, The Correct Option is (B) : 1.67
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- Qualitative Analysis
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.