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Mechanical Engineering Exam  >  Mechanical Engineering Tests  >  Test: Conditions of Equilibrium of a Floating & Submerged Bodies - Mechanical Engineering MCQ

Test: Conditions of Equilibrium of a Floating & Submerged Bodies - Mechanical Engineering MCQ


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10 Questions MCQ Test - Test: Conditions of Equilibrium of a Floating & Submerged Bodies

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

Detailed Solution for Test: Conditions of Equilibrium of a Floating & Submerged Bodies - Question 1

Explanation: 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.

Test: Conditions of Equilibrium of a Floating & Submerged Bodies - Question 2
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A solid cylinder of 15 cm diameter and 40 cm long, consists of two parts made of different materials. The first part at the base is 1.5 cm long and of specific gravity=6.5. The other part of the cylinder is made of the material having specific gravity 0.75. State, if the it can float vertically in water.

Detailed Solution for Test: Conditions of Equilibrium of a Floating & Submerged Bodies - Question 2

Explanation: AG=(weight of base*distance of C.G from base point A) + (weight of upper part*distance of C.G from point A)/ )weight of base + weight of upper part)
= 14.52
By principle of buoyancy,
Weight of cylinder = Weight of water displaced
h=38.625
AB=19.31
BG=14.25-19.31= -4.79
GM= Metacentric height=I/∀ -BG
= 6.16
As metacentric height is positive, it will float.

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Test: Conditions of Equilibrium of a Floating & Submerged Bodies - Question 3
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A wooden cylinder of sp.gr. = 0.6 and circular in cross-section is required to float in oil(sp.gr. = 0.90). Find the L/D ratio for the cylinder to float with its longitudinal axis vertical in oil, where L is the height of cylinder and D is its diameter.

Detailed Solution for Test: Conditions of Equilibrium of a Floating & Submerged Bodies - Question 3

Explanation: By principle of buoyancy,
Weight of cylinder = Weight of water displaced
h=2L/3
AG=L/2
AB=L/3
BG=AG-AB=L/6
GM= Metacentric height=I/∀ – BG=3D2/32L-L/6

For stable equilibrium, GM should be positive
GM>0
i.e L/D<3/4.

Test: Conditions of Equilibrium of a Floating & Submerged Bodies - Question 4
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A cylinder(uniform density distribution) of radius 3.0 m has a height of 9.0 m. The specific gravity of the material of cylinder 0.85 and it is floating in water with its axis vertical. State whether the equilibrium is stable or unstable.
Detailed Solution for Test: Conditions of Equilibrium of a Floating & Submerged Bodies - Question 4

Explanation: BG=Centre of pontoon – Centre of immersed portion=0.3-0.45*0.3=1.65
Metacentric height=I/∀ -BG
I=π*r⁴=π*3⁴
∀=π*r*r*h=π*3*3*9
Metacentric height=0.325.

Test: Conditions of Equilibrium of a Floating & Submerged Bodies - Question 5
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 If the magnitude of dimension of a rectangular wooden block is length>breadth>height, then for it to float on the water, it should be immersed in what manner?
Detailed Solution for Test: Conditions of Equilibrium of a Floating & Submerged Bodies - Question 5

When it is immersed in such a manner where height is partially immersed, its stability is most as moment of inertia is most about that axis.

Test: Conditions of Equilibrium of a Floating & Submerged Bodies - Question 6
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 When body is completely or partially immersed in a fluid, how much its weight be distributed for it to be in stable equilibrium.
Detailed Solution for Test: Conditions of Equilibrium of a Floating & Submerged Bodies - Question 6

Explanation: When the weight distribution is around the lower part, the centre of gravity is at lower portion and hence below the centre of buoyancy which is condition for stable equilibrium.

Test: Conditions of Equilibrium of a Floating & Submerged Bodies - Question 7
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In unstable equilibrium what is the relation between forces?
Detailed Solution for Test: Conditions of Equilibrium of a Floating & Submerged Bodies - Question 7

Explanation: Fb=W and the the centre of buoyancy is below the centre of gravity.

Test: Conditions of Equilibrium of a Floating & Submerged Bodies - Question 8
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 The floating body is said to be in unstable equilibrium if the metacentre is below the centre of gravity.
Detailed Solution for Test: Conditions of Equilibrium of a Floating & Submerged Bodies - Question 8

For a floating body

Metacentre above centre of gravity→ Stable Equilibrium

Metacentre coincides centre of gravity→ Neutral Equilibrium

Metacentre below centre of gravity→ Unstable Equilibrium

For a submerged body

Centre of buoyancy above centre of gravity→ Stable Equilibrium

Centre of buoyancy coincides centre of gravity→ Neutral Equilibrium

Centre of buoyancy below centre of gravity→ Unstable Equilibrium

Test: Conditions of Equilibrium of a Floating & Submerged Bodies - Question 9
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 The floating body is said to be in neutraL equilibrium if the metacentre is above the centre of gravity.
Detailed Solution for Test: Conditions of Equilibrium of a Floating & Submerged Bodies - Question 9

Explanation: The floating body is said to be in unstable equilibrium if the metacentre coincides with the centre of gravity.

Test: Conditions of Equilibrium of a Floating & Submerged Bodies - Question 10
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In stable equilibrium for completely submerged bodies what is the relation between forces?
Detailed Solution for Test: Conditions of Equilibrium of a Floating & Submerged Bodies - Question 10

Explanation: Fb=W and the the centre of buoyancy is above the centre of gravity.

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