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A rectangular lamina of width b and depth d is submerged vertically in water, such that the upper edge of the lamina is at a depth h from the free surface. What will be the expression for the depth of the centroid (G)?
- a)h
- b)h + d
- c)h + d ⁄ 2
- d)h + d / 2
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A rectangular lamina of width b and depth d is submerged vertically in...
Explanation: The centroid of the lamina will be located at it’s centre. ( d ⁄ 2). Thus, the depth of the centre of pressure will be h + d ⁄ 2.
Most Upvoted Answer
A rectangular lamina of width b and depth d is submerged vertically in...
B) h/2
The depth of the centroid (G) of a submerged rectangular lamina can be calculated using the formula:
h_G = h + (d/2) - (I_b/(bd^2)) * ρ_w
where h is the depth of the upper edge of the lamina from the free surface, d is the depth of the lamina, b is the width of the lamina, ρ_w is the density of water, and I_b is the second moment of area of the lamina about the horizontal axis passing through its centroid.
For a rectangular lamina, the second moment of area about the horizontal axis passing through its centroid can be calculated as:
I_b = (1/12) * b * d^3
Substituting this value and simplifying the equation for h_G, we get:
h_G = h + (d/2) - (ρ_w * b * d^2)/(12 * bd^2)
h_G = h + (d/2) - (ρ_w * d)/12
h_G = (2h + d)/2 - (ρ_w * d)/12
h_G = (2h + d - (ρ_w * d)/6)/2
Therefore, the expression for the depth of the centroid (G) is h_G = (2h + d - (ρ_w * d)/6)/2, which simplifies to h_G = h/2 + d/2 - (ρ_w * d)/12. Thus, the correct answer is b) h/2.
The depth of the centroid (G) of a submerged rectangular lamina can be calculated using the formula:
h_G = h + (d/2) - (I_b/(bd^2)) * ρ_w
where h is the depth of the upper edge of the lamina from the free surface, d is the depth of the lamina, b is the width of the lamina, ρ_w is the density of water, and I_b is the second moment of area of the lamina about the horizontal axis passing through its centroid.
For a rectangular lamina, the second moment of area about the horizontal axis passing through its centroid can be calculated as:
I_b = (1/12) * b * d^3
Substituting this value and simplifying the equation for h_G, we get:
h_G = h + (d/2) - (ρ_w * b * d^2)/(12 * bd^2)
h_G = h + (d/2) - (ρ_w * d)/12
h_G = (2h + d)/2 - (ρ_w * d)/12
h_G = (2h + d - (ρ_w * d)/6)/2
Therefore, the expression for the depth of the centroid (G) is h_G = (2h + d - (ρ_w * d)/6)/2, which simplifies to h_G = h/2 + d/2 - (ρ_w * d)/12. Thus, the correct answer is b) h/2.
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