MCQs on Metacentre and Metacentric Height

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

a
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.

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 m ?
a) 147.1 kN
b) 294.3 kN
c) 73.5 kN
d) 588.6 kN

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

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.
a) 0.506 m
b) 0.376 m
c) 1.012 m
d) 0.127 m

b
Explanation: BG= Centre of pontoon – Centre of immersed portion=0.4 – 0.55*0.8=0.04
Metacentric height=I/∀ -BG
I=bd³/12 = 3*2³/12
∀=3*2*0.8
Metacentric height=0.376 m.

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.
a) 1.9 m
b) 3.8 m
c) 5.7 m
d) .95 m

a
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.

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.
a) True
b) False

a
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.

Proper explanation for metacentre is:
a) Point at which line of action of force meets the normal axis of body when it is given angular displacement
b) Intersection of line passing through new centre of buoyancy and centre of gravity.
c) point about which body starts oscillating when it is given small angular displacement
d) All of the mentioned

d
Explanation: All of the above explanation are apt.

The metacentric height is affected by the change in density.
a) True
b) False

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

For a completely immersed body, the metacentric height is always zero.
a) True
b) False

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

Meta centre always lies below the centre of gravity
a) True
b) False

b
Explanation: It depends on the stability of floating body.

The principle of floatation of bodies is based on the premise of
a) Metacentre
b) Newtons first law
c) Newtons law of viscosity
d) None of the mentioned

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