Submerged Bodies MCQ Quiz - Objective Question with Answer for Submerged Bodies - Download Free PDF

Explanation:

Condition of stable equilibrium for a floating body in terms of metacentric height (GM) as follows:

• Stable equilibrium : GM > 0 (M is above G)
• Neutral equilibrium : GM = 0 (M coinciding with G)
• Unstable equilibrium : GM < 0 (M is below G)
   

The conditions of equilibrium of a floating body are: (1) stable (2) unstable and (3) neutral.

1. Stable condition.

• The equilibrium of a floating body is stable if there is a righting moment to restore it to its original position whenever it is given a small angular displacement.
• In such equilibrium, the metacenter lies above the center of gravity i.e. metacentric height is positive.
• The external couple is balanced by the couple developed by the internal forces.

2. Unstable condition.

• The equilibrium of a floating body is said to be unstable if any small tilting of the body is accompanied by the development of forces or moments which tend to further increase the displacement of the body. In unstable equilibrium, the metacenter (M) lies below the center of gravity (G) i.e. the metacentric height is negative.
• External applied couple and couple developed due to internal forces acting in the same direction, thereby increasing the displacement and making the equilibrium unstable.

3. Neutral condition.

• The equilibrium of a body is said to be neutral when on the small tilting of the body, the body takes a new position. In this equilibrium, the metacenter and center of gravity coincide.
• As neither a righting moment nor an overturning moment acts on the body, the body remains at rest a new position.

Explanation:

Stability of unconstrained Submerged Bodies in Fluid:

The equilibrium of a body submerged in a liquid requires that the weight of the body acting through its centre of gravity should be colinear with an equal hydrostatic lift acting through the centre of buoyancy.

• Stable Equilibrium: If the body returns to its original position by retaining the originally vertical axis as vertical
• Unstable Equilibrium: If the body does not return to its original position but moves further from it
• Neutral Equilibrium: If the body neither returns to its original position nor increases its displacement further, it will simply adopt its new position

The relative position of the centre of gravity (G) and centre of buoyancy (B) of a body determines the stability of a sub merged body.

• Stable Equilibrium: B is above G

• Unstable Equilibrium: B is below G

• Neutral Equilibrium: B coincides with G

For submerged body:

Stable Equilibrium: Centre of gravity is below than the centre of buoyancy

Unstable Equilibrium: Centre of gravity is above than the centre of buoyancy

Neutral Equilibrium: Centre of gravity coincides with the centre of buoyancy

One should know what stable and unstable equilibrium is

Let us suppose that a body is given a small angular displacement and then released. Then the body will be said to be in

Stable Equilibrium:

If the body returns to its original position by retaining the originally vertical axis as vertical.

Unstable Equilibrium:

Concept:

Buoyancy:

When a body is either wholly or partially immersed in a fluid, a lift is generated due to the net vertical component of hydrostatic pressure forces experienced by the body. This lift is called the buoyant force and the phenomenon is called buoyancy.

Centre of buoyancy:

The line of the buoyant force is vertical and passes through the center of gravity of the displaced fluid i.e. the centroid of the displaced volume which is known as the center of buoyancy. 

Important Points Archimedes principle:

The Archimedes principle states that the buoyant force on a submerged body is equal to the weight of the liquid displaced by the body and acts vertically upward through the centroid of the displaced volume.

Thus, the net weight of the submerged body, (the net vertical downward force experienced by it) is reduced from its actual weight by an amount that equals the buoyant force.

FB = ρghA = ρgV

FB = f(Vdisplaced, ρ)

Explanation:-

Buoyancy - 

When a body is either wholly or partially immersed in a fluid, the hydrostatic lift due to the net vertical component of the hydrostatic pressure forces experienced by the body is called the “Buoyant Force” and the phenomenon is called “Buoyancy”.

The Center of Buoyancy is a point through which the force of buoyancy is supposed to act.

When a body is submerged in a liquid (or a fluid), the equilibrium requires that the weight of the body acting through its Center of Gravity should be co-linear with the Buoyancy Force acting through the Center of Buoyancy.

If the Body is Not Homogeneous in its distribution of mass over the entire volume, the location of the Center of Gravity (G) does not coincide with the Center of Volume (B).

Depending upon the relative locations of (G) and (B), the submerged body attains different states of equilibrium: Stable, Unstable, and Neutral.

Stable Equilibrium:

(G) is located below (B).

A body is given a small angular displacement and then released, returns to its original position by retaining the original vertical axis as vertical because of the restoring couple produced by the action of the Buoyant Force and the Weight. 

Unstable Equilibrium:

(G) is located above (B).

Any disturbance from the equilibrium position will create a destroying couple that will turn the body away from the original position.

Neutral Equilibrium:

(G) and (B) coincide.

The body will always assume the same position in which it is placed. A body having a small displacement and then released, neither returns to the original position nor increases its displacement- It will simply adapt to the new position. 

Concept:

A body in a liquid is said to be stable when given small displacement, it returns to its original position.

For stability of completely submerged Bodies, the center of gravity ‘G’ is below the center of Buoyancy ‘B’.

Explanation:

Stability of unconstrained Submerged Bodies in Fluid:

The equilibrium of a body submerged in a liquid requires that the weight of the body acting through its centre of gravity should be colinear with an equal hydrostatic lift acting through the centre of buoyancy.

• Stable Equilibrium: If the body returns to its original position by retaining the originally vertical axis as vertical
• Unstable Equilibrium: If the body does not return to its original position but moves further from it
• Neutral Equilibrium: If the body neither returns to its original position nor increases its displacement further, it will simply adopt its new position

The relative position of the centre of gravity (G) and centre of buoyancy (B) of a body determines the stability of a sub merged body.

• Stable Equilibrium: B is above G

• Unstable Equilibrium: B is below G

• Neutral Equilibrium: B coincides with G

Concept:

Buoyancy:

When a body is either wholly or partially immersed in a fluid, a lift is generated due to the net vertical component of hydrostatic pressure forces experienced by the body. This lift is called the buoyant force and the phenomenon is called buoyancy.

Centre of buoyancy:

The line of the buoyant force is vertical and passes through the center of gravity of the displaced fluid i.e. the centroid of the displaced volume which is known as the center of buoyancy. 

Archimedes principle:

The Archimedes principle states that the buoyant force on a submerged body is equal to the weight of the liquid displaced by the body and acts vertically upward through the centroid of the displaced volume.

Thus, the net weight of the submerged body, (the net vertical downward force experienced by it) is reduced from its actual weight by an amount that equals the buoyant force.

FB = ρghA = ρgV

FB = f(Vdisplaced, ρ)

For submerged body:

Stable Equilibrium: Centre of gravity is below than the centre of buoyancy

Unstable Equilibrium: Centre of gravity is above than the centre of buoyancy

Neutral Equilibrium: Centre of gravity coincides with the centre of buoyancy

One should know what stable and unstable equilibrium is

Let us suppose that a body is given a small angular displacement and then released. Then the body will be said to be in

Stable Equilibrium:

If the body returns to its original position by retaining the originally vertical axis as vertical.

Unstable Equilibrium:

Explanation:-

Buoyancy - 

When a body is either wholly or partially immersed in a fluid, the hydrostatic lift due to the net vertical component of the hydrostatic pressure forces experienced by the body is called the “Buoyant Force” and the phenomenon is called “Buoyancy”.

The Center of Buoyancy is a point through which the force of buoyancy is supposed to act.

When a body is submerged in a liquid (or a fluid), the equilibrium requires that the weight of the body acting through its Center of Gravity should be co-linear with the Buoyancy Force acting through the Center of Buoyancy.

If the Body is Not Homogeneous in its distribution of mass over the entire volume, the location of the Center of Gravity (G) does not coincide with the Center of Volume (B).

Depending upon the relative locations of (G) and (B), the submerged body attains different states of equilibrium: Stable, Unstable, and Neutral.

Stable Equilibrium:

(G) is located below (B).

A body is given a small angular displacement and then released, returns to its original position by retaining the original vertical axis as vertical because of the restoring couple produced by the action of the Buoyant Force and the Weight. 

Unstable Equilibrium:

(G) is located above (B).

Any disturbance from the equilibrium position will create a destroying couple that will turn the body away from the original position.

Neutral Equilibrium:

(G) and (B) coincide.

The body will always assume the same position in which it is placed. A body having a small displacement and then released, neither returns to the original position nor increases its displacement- It will simply adapt to the new position. 

Concept:

A body in a liquid is said to be stable when given small displacement, it returns to its original position.

For stability of completely submerged Bodies, the center of gravity ‘G’ is below the center of Buoyancy ‘B’.

The point ' M ' at which the line of action of the new buoyant force intersects the original vertical through the CG of the body, is called the meta-centre. It is a point about which a floating body starts oscillating when given a small angular displacement.

Concept:

Condition of stable equilibrium for a submerged body in terms of center of buoyancy and the center of gravity:

• Stable equilibrium: If its center of gravity is directly below the center of buoyancy
• Neutral equilibrium: If its center of gravity is coincident with the center of buoyancy
• Unstable equilibrium: If its center of gravity is directly above the center of buoyancy

Condition of stable equilibrium for a floating body in terms of metacentric height (GM) as follows:

• Stable equilibrium: GM > 0 (M is above G) i.e. Metacentric height is positive.
• Neutral equilibrium : GM = 0 (M coinciding with G)
• Unstable equilibrium : GM < 0 (M is below G)

Explanation:

The Centre of pressure is defined as the point of application of the total pressure on the surface.

The point of action of the total hydrostatic force on the submerged surface is called the Centre of Pressure.

G = Centre of gravity of plane surface

P = Centre of pressure

Meta Centre is defined as the point about which a body starts oscillating when body is tilted by a small angle. The meta-centre may also be defined as the point at which the line of action of the force of buoyancy will meet the normal axis of the body when the body is given a small angular displacement.

The distance MG i.e. the distance between the meta-centre of a floating body and the centre of gravity of the body is called meta-centric height. It is measured along the line BG.

When a solid body is either wholly or partially immersed in a fluid, the hydrostatic lift due to net vertical component of the hydrostatic pressure forces experienced by the body is called the buoyant force. The buoyant force on a submerged or floating body is equal to the weight of the liquid displaced by the body and acts vertically upward through the centroid of a displaced volume known as the centre of buoyancy.

Centre of gravity is the point in the body or system around which mass or weight is evenly distributed and through which the force of gravity acts.

Explanation:

Stability of unconstrained Submerged Bodies in Fluid:

The equilibrium of a body submerged in a liquid requires that the weight of the body acting through its centre of gravity should be colinear with an equal hydrostatic lift acting through the centre of buoyancy.

• Stable Equilibrium: If the body returns to its original position by retaining the originally vertical axis as vertical
• Unstable Equilibrium: If the body does not return to its original position but moves further from it
• Neutral Equilibrium: If the body neither returns to its original position nor increases its displacement further, it will simply adopt its new position

The relative position of the centre of gravity (G) and centre of buoyancy (B) of a body determines the stability of a submerged body.

• Stable Equilibrium: B is above G

• Unstable Equilibrium: B is below G

• Neutral Equilibrium: B coincides with G