Fluid Mechanics Multiple Choice Questions & Answers on “Conditions of Equilibrium of a Floating and Submerged Bodies”.
1. 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
Answer: b
Clarification: 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.
2. 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.
a) It will float
b) It will not float
c) Data insufficient
d) None of the mentioned
Answer: a
Clarification: 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.
3. 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.
a) L/D<9/16
b) L/D<3/4
c) L/D<2/3
d) None of the mentioned
Answer: b
Clarification: 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.
4. 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.
a) Stable
b) Unstable
c) Insufficient Data
d) None of the mentioned
Answer: a
Clarification: 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.
5. 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?
a) It should be immersed vertically such that length is partially immersed
b) It should be immersed horizontally such that breadth is partially immersed
c) It should be immersed such that height is partially immersed
d) None of the mentioned
Answer: b
Clarification: 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.
6. When body is completely or partially immersed in a fluid, how much its weight be distributed for it to be in stable equilibrium.
a) Around the lower part
b) Around the upper part
c) Is independent of weight distribution
d) None of the mentioned
Answer: a
Clarification: 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.
7. In unstable equilibrium what is the relation between forces?
a) Buoyancy force= Weight of body
b) Buoyancy force > Weight of body
c) Buoyancy force < Weight of body
d) None of the mentioned
Answer: a
Clarification: Fb=W and the the centre of buoyancy is below the centre of gravity.
8. The floating body is said to be in unstable equilibrium if the metacentre is below the centre of gravity.
a) True
b) False
Answer: b
Clarification: The floating body is said to be in unstable equilibrium if the metacentre is above the centre of gravity.
9. The floating body is said to be in neutraL equilibrium if the metacentre is above the centre of gravity.
a) True
b) False
Answer: b
Clarification: The floating body is said to be in unstable equilibrium if the metacentre coincides with the centre of gravity.
10. In stable equilibrium for completely submerged bodies what is the relation between forces?
a) Buoyancy force= Weight of body,the centre of buoyancy is below the centre of gravity.
b) Buoyancy force=Weight of body, the centre of buoyancy is above the centre of gravity.
c) Buoyancy force < Weight of body
d) None of the mentioned
Answer: b
Clarification: Fb=W and the the centre of buoyancy is above the centre of gravity.
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