Question:
The two femurs each of cross-sectional area $10 \,cm^{2}$ support the upper part of a human body of mass $40\, kg$. The average pressure sustained by the femurs is $(Take\, g = 10\, m\, s^{-2})$
The two femurs each of cross-sectional area $10 \,cm^{2}$ support the upper part of a human body of mass $40\, kg$. The average pressure sustained by the femurs is $(Take\, g = 10\, m\, s^{-2})$
Updated On: Jul 7, 2022
- $2 \times 10^{3} N \, m^{-2}$
- $2 \times 10^{4} \, N \, m^{-2}$
- $2 \times 10^{5} \, N\, m^{-2}$
- $2 \times 10^{6} \, N \, m^{-2}$
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The Correct Option is C
Solution and Explanation
Total cross-sectional area of the femurs is,
$A=2 \times 10\, cm^{2} =2 \times 10 \times 10^{-4} m^{2}=20 \times 10^{-4} \, m^{2}$
Force acting on them is
$F = mg = 40 \,kg \times 10\, m \,s^{-2} = 400 \,N$
$\therefore\quad$ Average pressure sustained by them is
$P=\frac{F}{A}=\frac{400 \,N}{20\times10^{-4} \,m^{2}}=2\times10^{5}\, N \, m^{-2}\quad$
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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.