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A solid cylinder of diameter 5.0 m has a height of 6.0 m. Find the meta-centric height of the cylinder if the specific gravity of the material of cylinder 0.45 and it is floating in water with its axis vertical. State whether the equilibrium is stable or unstable.
  • a)
    -0.29 m
  • b)
    -0.61 m
  • c)
    -1.16 m
  • d)
    0.14 m
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A solid cylinder of diameter 5.0 m has a height of 6.0 m. Find the met...
 BG=Centre of pontoon – Centre of immersed portion=0.3-0.45*0.3=1.65
Metacentric height=I/∀ -BG
I=π*r⁴=π*2.5⁴
∀=π*r*r*h=π*2.5*2.5*6
Metacentric height=-0.61.
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Most Upvoted Answer
A solid cylinder of diameter 5.0 m has a height of 6.0 m. Find the met...
Given:
Diameter of cylinder = 5.0 m
Height of cylinder = 6.0 m
Specific gravity of material of cylinder = 0.45
Meta-centric height of the cylinder = ?
Axis of cylinder is vertical

To find:
Meta-centric height of the cylinder and stability of equilibrium

Solution:

The meta-centric height (GM) of the cylinder can be calculated using the formula:

GM = I / V

Where,
I = Moment of inertia of the cylinder
V = Volume of displaced water

The moment of inertia of the cylinder can be calculated using the formula:

I = (π / 4) × r^4
Where,
r = radius of the cylinder = 2.5 m

I = (π / 4) × (2.5)^4
I = 76.17 m^4

The volume of displaced water can be calculated using the formula:

V = π/4 × d^2 × h
Where,
d = diameter of the cylinder = 5.0 m
h = height of the cylinder = 6.0 m

V = π/4 × (5.0)^2 × 6.0
V = 88.36 m^3

GM = I / V
GM = 76.17 / 88.36
GM = -0.86 m

Since the meta-centric height (GM) is negative, the equilibrium is unstable.

Therefore, the correct option is (B) -0.61 m.
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A solid cylinder of diameter 5.0 m has a height of 6.0 m. Find the meta-centric height of the cylinder if the specific gravity of the material of cylinder 0.45 and it is floating in water with its axis vertical. State whether the equilibrium is stable or unstable.a)-0.29 mb)-0.61 mc)-1.16 md)0.14 mCorrect answer is option 'B'. Can you explain this answer?
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A solid cylinder of diameter 5.0 m has a height of 6.0 m. Find the meta-centric height of the cylinder if the specific gravity of the material of cylinder 0.45 and it is floating in water with its axis vertical. State whether the equilibrium is stable or unstable.a)-0.29 mb)-0.61 mc)-1.16 md)0.14 mCorrect answer is option 'B'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A solid cylinder of diameter 5.0 m has a height of 6.0 m. Find the meta-centric height of the cylinder if the specific gravity of the material of cylinder 0.45 and it is floating in water with its axis vertical. State whether the equilibrium is stable or unstable.a)-0.29 mb)-0.61 mc)-1.16 md)0.14 mCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid cylinder of diameter 5.0 m has a height of 6.0 m. Find the meta-centric height of the cylinder if the specific gravity of the material of cylinder 0.45 and it is floating in water with its axis vertical. State whether the equilibrium is stable or unstable.a)-0.29 mb)-0.61 mc)-1.16 md)0.14 mCorrect answer is option 'B'. Can you explain this answer?.
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