A floating body is said to be in a state of stable equilibrium

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

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

For the conditions of the equilibrium of the body, i.e. the rigid body only the external forces defines the equilibrium. And the support reactions only cancels out the rotation part of the body and thus the potential energy of the body is stored in it.

A

The first part of the statement is false and other part is true

B

The first part of the statement is false and other part is false too

C

The first part of the statement is true and other part is false

D

The first part of the statement is true and other part is true too

In which of the following case we can surely say that the body A is charged: a) When a positively charged body is kept near to body A and it gets attracted b) When a negatively charged body is kept near to body A and it gets attracted c) When a positively charged body is kept near to body A and it gets repelled

A

Only in case a the body A is surely charged

B

Only in case b the body A is surely charged

C

Only in case c the body A is surely charged

D

In all the cases a, b and c the body A is surely charged

In a town fair 50 people were asked which dessert they liked: ice cream, Donuts, or cupcakes. 28 said they like ice cream, 26 said they like donuts, and 26 said they like cupcakes. 8 said they like all three. 17 said they like donuts and cupcakes, 11 said they like ice cream and cupcakes. 5 said they do not like any of these. Find those people who liked ice cream and donuts but not cupcakes.

A

10

B

7

C

5

D

9

E

None of the above

If a body floating in a liquid occupies a new position and remains at rest in this new position, when given a small angular displacement, the body is said to be in __________ equilibrium.

A

Neutral

B

Stable

C

Unstable

D

None of these

The conditions for the stable equilibrium of a floating body are

A

The metacentre should lie above the center of gravity

B

The center of buoyancy and the center of gravity must lie on the same vertical line

C

A righting couple should be formed

D

All the above are correct

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 body will be in a stable equilibrium in a floating condition if

A

The metacenter is below the centre of gravity

B

The metacenter is above the centre of gravity

C

The metacentric height is zero

D

The centre of buoyancy coincide with the cnetre of gravity

E

The metacenter coincide with the centre of buoyancy

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

A floating body is said to be in a state of stable equilibrium

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