The floating body is said to be in unstable equilibrium if the metacentre is below the centre of gravity.

The following terms relate to floating bodies: where G = Centre of gravity, M = Meta Centre, W = Weight of floating body, FB = Buoyant force. Match List-I with List-II and select the correct answer. List-I (Condition) List-II (Result) A. G is above M 1. Stable equilibrium B. G and M coincide 2. Unstable equilibrium C. G is below M 3. Floating body D. FB ≥ W 4. Neutral equilibrium

A

A-1, B-3, C-2, D-4

B

A-3, B-1, C-4, D-2

C

A-2, B-4, C-1, D-3

D

A-2, B-3, C-4, D-1

If B = centre of buoyancy, G = centre of gravity, B1 = new centre of buoyancy when the floating body rotates by an angle θ, then the location of metacentre will be:

A

in between point B and B₁

B

at the point of intersection of axis of floating body passing through B and G and vertical line passing through B₁

C

at the point of intersection of axis of floating body passing through B and G and horizontal line passing through B₁

D

same as B₁

The floating body is said to be in neutraL equilibrium if the metacentre is above the centre of gravity.

A

True

B

False

For a floating body to be in a stable equilibrium, where G is the centre of gravity, B is the center of buoyancy and M is the metacentre, which of the following statements is true?

A

M and G coincide

B

M is below G

C

M is above G

D

M and B coincide

For an unstable equilibrium of a floating body (where, M = metacentre.)

A

M is above G

B

M is below G

C

M & G coincide

D

None of these

Consider the following statements pertaining to stability of floating bodies: 1) A floating body will be stable when the centre of gravity is above the centre of buoyancy. 2) The positions of metacentres corresponding to different axes of rotation are generally different for the same floating object. 3) For cargo ships, the metacentric height varies with loading. Which of the above statements are correct?

A

1, 2 and 3

B

1 and 2 only

C

1 and 3 only

D

2 and 3 only

A body floating in a liquid is said to be in neutral equilibrium, if its metacentre

A

Coincides with its centre of gravity

B

Lies above its centre of gravity

C

Lies below its centre of gravity

D

Lies between the centre of buoyancy and centre of gravity

For a floating body to be in stable equilibrium, its metacentre should be

A

below the center of buoyancy

B

above the center of buoyancy

C

between e.g. and center of pressure

D

above the center of gravity.

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

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

The floating body is said to be in unstable equilibrium if the metacentre is below the centre of gravity.

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