Question:
A beaker of radius 6 cm is filled with mercury up to a height to 12 cm. Given that the density of mercury is $ 13600\text{ }kg/{{m}^{3}}, $ the force exerted by the mercury on the bottom of the beaker is approximately.
A beaker of radius 6 cm is filled with mercury up to a height to 12 cm. Given that the density of mercury is $ 13600\text{ }kg/{{m}^{3}}, $ the force exerted by the mercury on the bottom of the beaker is approximately.
Updated On: Feb 22, 2024
- 184 N
- 1100N
- 1200 N
- 1300 N
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The Correct Option is A
Solution and Explanation
: Pressure of mercury on bottom $ =dgh $ $ P=13600\times 10\times \frac{12}{100}N{{m}^{-2}} $ Area of bottom $ =\pi {{R}^{2}}=3.14\times {{\left( \frac{6}{100} \right)}^{2}}{{m}^{2}} $ $ \therefore $ Force = Pressure $ \times $ area or Force $ =\frac{13600\times 10\times 12\times 3.14\times 36}{100\times 100\times 100}N $ or Force = 184.48 N.
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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.