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Question:
A boy has $60\, kg$ weight. He wants to swim in a river with the help of a wooden log. If relative density of wood is $0.6$. What is the minimum volume of wooden log? (Density of river water is $1000\, kg / m ^{3}$ )
A boy has $60\, kg$ weight. He wants to swim in a river with the help of a wooden log. If relative density of wood is $0.6$. What is the minimum volume of wooden log? (Density of river water is $1000\, kg / m ^{3}$ )
Updated On: Sep 22, 2024
- $ 0.66\,m^{3}$
- $ 150\,m^{3}$
- $ \frac{3}{1}\,m^{3}$
- $ \frac{3}{20}\,m^{3}$
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The Correct Option is D
Solution and Explanation
From Archimedes principle Weight of (boy + log) = weight of water displaced $ (60+V \times 0.6 \times 10^{3})g=V \times 10^{3} g $
$\Rightarrow 0.4 \times 10^{3}V=60$
$ \Rightarrow V=\frac{60}{0.4 \times 10^{3}}=\frac{600}{400}=\frac{3}{20}m^{3}$
$\Rightarrow 0.4 \times 10^{3}V=60$
$ \Rightarrow V=\frac{60}{0.4 \times 10^{3}}=\frac{600}{400}=\frac{3}{20}m^{3}$
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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.
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