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.

The depth of centre of pressure (h) for a vertically immersed surface from the liquid surface is given by (where IG = Moment of inertia of the immersed surface about horizontal axis through its centre of gravity, A = Area of immersed surface, and x = Depth of centre of gravity of the immersed surface from the liquid surface)

A

(IG/Ax̅) - x̅

B

(IG/x̅) - Ax̅

C

(Ax̅/IG) + x̅

D

(IG/Ax̅) + x̅

The depth of centre of pressure (h) for a vertically immersed surface from the liquid surface is given by (where $${I_{\text{G}}}$$ = Moment of inertia of the immersed surface about horizontal axis through its centre of gravity, A = Area of immersed surface and x = Depth of centre of gravity of the immersed surface from the liquid surface)

A

$$\frac{{{I_{\text{G}}}}}{{{\text{A}}\overline {\text{x}} }} - \overline {\text{x}} $$

B

$$\frac{{{I_{\text{G}}}}}{{\overline {\text{x}} }} - {\text{A}}\overline {\text{x}} $$

C

$$\frac{{{\text{A}}\overline {\text{x}} }}{{{I_{\text{G}}}}} + \overline {\text{x}} $$

D

$$\frac{{{I_{\text{G}}}}}{{{\text{A}}\overline {\text{x}} }} + \overline {\text{x}} $$

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

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

All objects experience a buoyancy when they are immersed in a fluid. Buoyancy is

A

a downward force

B

a downward pressure

C

an upward force

D

an upward pressure

A vertically immersed surface is shown in the below figure. The distance of its centre of pressure from the water surface is
Hydraulics and Fluid Mechanics in ME mcq question image

Hydraulics and Fluid Mechanics in ME mcq question image

A

$$\frac{{{\text{b}}{{\text{d}}^2}}}{{12}} + \overline {\text{x}} $$

B

$$\frac{{{{\text{d}}^2}}}{{12\overline {\text{x}} }} + \overline {\text{x}} $$

C

$$\frac{{{{\text{b}}^2}}}{{12}} + \overline {\text{x}} $$

D

$$\frac{{{{\text{d}}^2}}}{{12}} + \overline {\text{x}} $$

The total pressure on a horizontally immersed surface is (where w = Specific weight of the liquid, A = Area of the immersed surface, and x = Depth of the centre of gravity of the immersed surface from the liquid surface)

A

wA

B

wx

C

wAx

D

wA/x

The total pressure on a horizontally immersed surface is (where w = Specific weight of the liquid, A = Area of the immersed surface and x = Depth of the centre of gravity of the immersed surface from the liquid surface)

A

wA

B

wx

C

wAx

D

$$\frac{{{\text{wA}}}}{{\text{x}}}$$

Bernoulli's equation for fluid flow is derived following certain assumptions. Out of the assumptions listed below, which set of assumptions is used in derivation of Bernoulli's equation?
1. Fluid flow is frictionless & irrotational
2. Fluid flow is steady
3. Fluid flow is uniform & turbulent
4. Fluid is compressible
5. Fluid is incompressible

A

1, 3, 4

B

2, 4, 5

C

1, 2, 5

D

1, 4, 5

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.

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