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A rectangular pontoon is 5 m long, 3 m wide and 1.40 m high. The depth of immersion of the pontoon is 0.60 m in seawater. If the centre of gravity is 0.7 m above the bottom of the pontoon, determine the metacentric height. The density for seawater = 1045 kg/m3
  • a)
    0.135
  • b)
    0.271
  • c)
    0.543
  • d)
    0.068
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A rectangular pontoon is 5 m long, 3 m wide and 1.40 m high. The depth...
Explanation: BG=Centre of pontoon – Centre of immersed portion=0.7-0.3=0.4
Metacentric height=I/∀ -BG
I=bd³/12 = 5*3³/12
∀=5*3*1.4
Metacentric height=0.135 m.
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Most Upvoted Answer
A rectangular pontoon is 5 m long, 3 m wide and 1.40 m high. The depth...
Given data:
Length of the pontoon (l) = 5 m
Width of the pontoon (b) = 3 m
Height of the pontoon (h) = 1.4 m
Depth of immersion (d) = 0.6 m
Centre of gravity (G) = 0.7 m above the bottom
Density of seawater (ρ) = 1045 kg/m³

To find: Metacentric height (GM)

Formula used:
Metacentric height (GM) = I / V * (1 / ρ)
where,
I = Moment of inertia of water plane
V = Volume of the displaced water

Calculation:
1. Volume of the displaced water:
Volume of the pontoon = l * b * h = 5 * 3 * 1.4 = 21 m³
Volume of the displaced water = l * b * d = 5 * 3 * 0.6 = 9 m³

2. Moment of inertia of the water plane:
I = b * d³ / 12 = 3 * 0.6³ / 12 = 0.0648 m⁴

3. Metacentric height:
GM = I / V * (1 / ρ) = 0.0648 / 9 * (1 / 1045) = 0.135 m

Therefore, the metacentric height of the pontoon is 0.135 m. Hence, option (a) is the correct answer.
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A rectangular pontoon is 5 m long, 3 m wide and 1.40 m high. The depth...
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A rectangular pontoon is 5 m long, 3 m wide and 1.40 m high. The depth of immersion of the pontoon is 0.60 m in seawater. If the centre of gravity is 0.7 m above the bottom of the pontoon, determine the metacentric height. The density for seawater = 1045 kg/m3.a)0.135b)0.271c)0.543d)0.068Correct answer is option 'A'. Can you explain this answer?
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A rectangular pontoon is 5 m long, 3 m wide and 1.40 m high. The depth of immersion of the pontoon is 0.60 m in seawater. If the centre of gravity is 0.7 m above the bottom of the pontoon, determine the metacentric height. The density for seawater = 1045 kg/m3.a)0.135b)0.271c)0.543d)0.068Correct answer is option 'A'. 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 rectangular pontoon is 5 m long, 3 m wide and 1.40 m high. The depth of immersion of the pontoon is 0.60 m in seawater. If the centre of gravity is 0.7 m above the bottom of the pontoon, determine the metacentric height. The density for seawater = 1045 kg/m3.a)0.135b)0.271c)0.543d)0.068Correct answer is option 'A'. 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 rectangular pontoon is 5 m long, 3 m wide and 1.40 m high. The depth of immersion of the pontoon is 0.60 m in seawater. If the centre of gravity is 0.7 m above the bottom of the pontoon, determine the metacentric height. The density for seawater = 1045 kg/m3.a)0.135b)0.271c)0.543d)0.068Correct answer is option 'A'. Can you explain this answer?.
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