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?

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 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

From the data given: 54tr xc Connecting rod of mass 2 kg and the distance between the centre of crank and centre of gudgeon pin is 25 cm. The Center of Gravity lies at a point 10 cm from the gudgeon pin along the line of centres. The radius of gyration of this system about an axis through the Center of Gravity perpendicular to the plane of rotation is 11 cm. Find the mass placed at distance l2 from center of gravity.

A

0.9

B

0.8

C

1.1

D

1.2

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

A

True

B

False

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

A

True

B

False

A submerged body is said to be in a stable equilibrium, if its centre of gravity __________ the centre of buoyancy.

A

Coincides with

B

Lies below

C

Lies above

D

None of these

The curve of metacentre for a floating body __________ the curve of buoyancy.

A

Is always below

B

Is the evolute of

C

Intersects at right angle

D

Is tangential to

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.

Given steps in procedure to find the center of gravity of the quadrilateral ABCD. Arrange the steps. i. Draw lines joining G1 with G2 and G3 with G4. ii. In given quadrilateral draw diagonal BD and locate centers of gravity G1, G2 of triangles BCD and ABD. iii. The point of intersection of lines G1G2 and G3G4 gives the center of gravity of the quadrilateral ABCD. iv. Similarly draw the diagonal AC and determine the centers of gravity G3, G4 of triangles ABC and ADC.

A

i, ii, iii, iv

B

ii, iv, i, iii

C

iii, iv, i, ii

D

iv, i, ii, iii

GM > 0 (Metacentre is above centre of Gravity)	Stable equilibrium
GM = 0 (Metacentre coinciding with centre of Gravity)	Neutral equilibrium
GM < 0 (Metacentre is below centre of Gravity)	Unstable equilibrium

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?

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