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The total pressure on the top of a closed cylindrical vessel completely filled up with a liquid is
Answer & Solution
Correct Answer:
Option
C
The total pressure on the top of a closed cylindrical vessel completely filled with a liquid is directly proportional to (radius)4. This phenomenon is a result of the distribution of pressure in a fluid due to its weight.
When a vessel is completely filled with liquid, the pressure at a specific depth is determined by the weight of the liquid above that level. The pressure at any point within a static fluid is proportional to the height of the fluid column above that point. For a cylindrical vessel, the pressure distribution is influenced by the cross-sectional area, which is proportional to the square of the radius.
Since the pressure is directly related to the height of the liquid column and the area of the cross-section (which is proportional to the radius squared), the total pressure on the top of the vessel will be directly proportional to (radius)2 * (radius)2, which simplifies to (radius)4.
When a vessel is completely filled with liquid, the pressure at a specific depth is determined by the weight of the liquid above that level. The pressure at any point within a static fluid is proportional to the height of the fluid column above that point. For a cylindrical vessel, the pressure distribution is influenced by the cross-sectional area, which is proportional to the square of the radius.
Since the pressure is directly related to the height of the liquid column and the area of the cross-section (which is proportional to the radius squared), the total pressure on the top of the vessel will be directly proportional to (radius)2 * (radius)2, which simplifies to (radius)4.
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LoginP=r2 is right
h=ω^2r^2/2g.
A=πr^2.
So, P=r^4.