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A circular disc of diameter D is immersed vertically in a liquid of density p. The top most point of the disc just touches the liquid surface . What is depth of center of pressure ?
- a)3D/8
- b)5D/8
- c)D/2
- d)2D/3
Correct answer is option 'B'. Can you explain this answer?
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A circular disc of diameter D is immersed vertically in a liquid of de...
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A circular disc of diameter D is immersed vertically in a liquid of de...
Explanation:
Center of Pressure:
The center of pressure is the point on a submerged surface where the resultant force acts vertically upwards.
Calculation:
- The depth of the center of pressure can be determined using the principle of hydrostatic pressure.
- The pressure at the topmost point of the disc is atmospheric pressure.
- The pressure at the center of the disc can be calculated using the hydrostatic pressure formula: P = pgh, where p is the density of the liquid, g is the acceleration due to gravity, and h is the depth.
- The pressure at the center of the disc is equal to the pressure at the topmost point of the disc, as the disc is in equilibrium.
- By equating the two pressures, we can find the depth of the center of pressure.
Calculation Steps:
1. Pressure at the topmost point of the disc = Atmospheric pressure = 0
2. Pressure at the center of the disc = pgh
3. Equating the two pressures: pgh = 0
4. Solving for h: h = 0
5. The depth of the center of pressure is 0, which means it is at the same level as the topmost point of the disc.
Therefore, the depth of the center of pressure is 0, which corresponds to the topmost point of the disc just touching the liquid surface.
Center of Pressure:
The center of pressure is the point on a submerged surface where the resultant force acts vertically upwards.
Calculation:
- The depth of the center of pressure can be determined using the principle of hydrostatic pressure.
- The pressure at the topmost point of the disc is atmospheric pressure.
- The pressure at the center of the disc can be calculated using the hydrostatic pressure formula: P = pgh, where p is the density of the liquid, g is the acceleration due to gravity, and h is the depth.
- The pressure at the center of the disc is equal to the pressure at the topmost point of the disc, as the disc is in equilibrium.
- By equating the two pressures, we can find the depth of the center of pressure.
Calculation Steps:
1. Pressure at the topmost point of the disc = Atmospheric pressure = 0
2. Pressure at the center of the disc = pgh
3. Equating the two pressures: pgh = 0
4. Solving for h: h = 0
5. The depth of the center of pressure is 0, which means it is at the same level as the topmost point of the disc.
Therefore, the depth of the center of pressure is 0, which corresponds to the topmost point of the disc just touching the liquid surface.
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A circular disc of diameter D is immersed vertically in a liquid of density p. The top most point of the disc just touches the liquid surface . What is depth of center of pressure ?a)3D/8b)5D/8c)D/2d)2D/3Correct answer is option 'B'. Can you explain this answer?
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