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Mechanical Engineering Exam  >  Mechanical Engineering Tests  >  Test: Metacentre & Metacentric Height - Mechanical Engineering MCQ

Test: Metacentre & Metacentric Height - Mechanical Engineering MCQ


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10 Questions MCQ Test - Test: Metacentre & Metacentric Height

Test: Metacentre & Metacentric Height for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Test: Metacentre & Metacentric Height questions and answers have been prepared according to the Mechanical Engineering exam syllabus.The Test: Metacentre & Metacentric Height MCQs are made for Mechanical Engineering 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Metacentre & Metacentric Height below.
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Test: Metacentre & Metacentric Height - Question 1
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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. 

Detailed Solution for Test: Metacentre & Metacentric Height - Question 1

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.

Test: Metacentre & Metacentric Height - Question 2
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A uniform body of size 4 m long * 2.5 m wide * 1.5 m deep floats in water. What is the weight of the body if depth of immersion is 1.5 m ?

Detailed Solution for Test: Metacentre & Metacentric Height - Question 2

Explanation: Weight of Body = Weight of water displaced
= ρ*g*Volume of displaced water=9.81*1000*4*2.5*1.5=147.1kN.

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Test: Metacentre & Metacentric Height - Question 3
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A block of material of specific gravity 0.45 floats in water. Determine the meta-centric height of the block if its size is 3 m * 2 m* 0.8 m.

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Test: Metacentre & Metacentric Height - Question 4
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A solid cylinder of diameter 4.5 has a height of 2.5 metres. Find the meta-centric height of the cylinder when it is floating in water with its axis vertical. The sp. gr. of the cylinder=0.45.
Detailed Solution for Test: Metacentre & Metacentric Height - Question 4

Explanation:BG= Centre of pontoon – Centre of immersed portion=1.25-0.45*2.5=0.125
Metacentric height=I/∀ -BG
I=π*r⁴
∀= π*r*r*h
Metacentric height=1.9 m.

Test: Metacentre & Metacentric Height - Question 5
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In case of spherically shaped bodies of uniform mass distribution and completely immersed in fluid and floating, the centre of buoyancy coincides with centre of gravity.
Detailed Solution for Test: Metacentre & Metacentric Height - Question 5

Explanation: The volume of fluid displaced by the body is equal to the actual volume of body in air. Hence, In case of spherically shaped bodies of uniform mass distribution and completely immersed in fluid and floating, the centre of buoyancy coincides with centre of gravity.

Test: Metacentre & Metacentric Height - Question 6
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Proper explanation for metacentre is:
Detailed Solution for Test: Metacentre & Metacentric Height - Question 6

Explanation: All of the above explanation are apt.

Test: Metacentre & Metacentric Height - Question 7
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 The metacentric height is affected by the change in density.
Detailed Solution for Test: Metacentre & Metacentric Height - Question 7

Explanation: Metacentre does depend on the density. Hence, the metacentric height is affected by the change in density.

Test: Metacentre & Metacentric Height - Question 8
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For a completely immersed body, the metacentric height is always zero.
Detailed Solution for Test: Metacentre & Metacentric Height - Question 8

Explanation: The metacentric height may or may not be zero as metacentre will not always coincide with centre of gravity.

Test: Metacentre & Metacentric Height - Question 9
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Meta centre always lies below the centre of gravity
Detailed Solution for Test: Metacentre & Metacentric Height - Question 9

Explanation: It depends on the stability of floating body.

Test: Metacentre & Metacentric Height - Question 10
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The principle of floatation of bodies is based on the premise of
Detailed Solution for Test: Metacentre & Metacentric Height - Question 10

Explanation: The principle of floatation of bodies is based on the premise of Metacentre.

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