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The depth of centre of pressure for a rectangular laminaimmersed vertically in water up to height ‘h’ is given by:
- a)h/2
- b)h/4
- c)2h/3
- d)3h/2
Correct answer is option 'C'. Can you explain this answer?
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The depth of centre of pressure for a rectangular laminaimmersed verti...
Ans. (c)
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The depth of centre of pressure for a rectangular laminaimmersed verti...
Explanation:
Centre of Pressure:
- The centre of pressure of a submerged rectangular lamina is the point where the total pressure acts vertically downward.
- It is located at a distance 'h/3' from the free surface of the liquid, where 'h' is the height of the lamina immersed in the liquid.
Formula:
- The depth of the centre of pressure for a submerged rectangular lamina is given by the formula: Depth = (2h)/3.
Derivation:
- The total pressure on the submerged surface is equal to the weight of the liquid above it.
- The pressure at a depth 'h' in a liquid is given by the formula: P = ρgh, where ρ is the density of the liquid and g is the acceleration due to gravity.
- The total pressure on the lamina is given by: P_total = ρgh^2.
- The depth of the centre of pressure is calculated by dividing the total pressure by the weight density of the liquid: Depth = P_total / (ρg).
- Substituting the values, we get: Depth = (ρgh^2) / (ρg) = h^2 / h = h/3.
Therefore, the depth of the centre of pressure for a rectangular lamina immersed vertically in water up to height h is 2h/3.
Centre of Pressure:
- The centre of pressure of a submerged rectangular lamina is the point where the total pressure acts vertically downward.
- It is located at a distance 'h/3' from the free surface of the liquid, where 'h' is the height of the lamina immersed in the liquid.
Formula:
- The depth of the centre of pressure for a submerged rectangular lamina is given by the formula: Depth = (2h)/3.
Derivation:
- The total pressure on the submerged surface is equal to the weight of the liquid above it.
- The pressure at a depth 'h' in a liquid is given by the formula: P = ρgh, where ρ is the density of the liquid and g is the acceleration due to gravity.
- The total pressure on the lamina is given by: P_total = ρgh^2.
- The depth of the centre of pressure is calculated by dividing the total pressure by the weight density of the liquid: Depth = P_total / (ρg).
- Substituting the values, we get: Depth = (ρgh^2) / (ρg) = h^2 / h = h/3.
Therefore, the depth of the centre of pressure for a rectangular lamina immersed vertically in water up to height h is 2h/3.
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The depth of centre of pressure for a rectangular laminaimmersed vertically in water up to height ‘h’ is given by:a)h/2b)h/4c)2h/3d)3h/2Correct answer is option 'C'. Can you explain this answer?
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