For a completely submerged body with centre of gravity G and centre of...
Stability of a completely submerged body is determined by the relative positions of its center of gravity (G) and its center of buoyancy (B). The center of gravity is the point at which the entire weight of the body is considered to act, while the center of buoyancy is the point at which the buoyant force (equal to the weight of the fluid displaced by the body) is considered to act.
The stability of a completely submerged body can be determined by considering what happens when the body is displaced from its equilibrium position. If the body is stable, it will tend to return to its original position when displaced. If it is unstable, it will tend to move further away from its original position when displaced.
A. G is located below B:
If the center of gravity (G) is located below the center of buoyancy (B), the body will be stable. When the body is displaced, a restoring torque is generated that tends to return the body to its original position. This is because the weight of the body acts downwards through G, while the buoyant force acts upwards through B. The difference in these forces creates a torque that causes the body to rotate back to its original orientation.
B. G is located above B:
If the center of gravity (G) is located above the center of buoyancy (B), the body will be unstable. When the body is displaced, a destabilizing torque is generated that tends to move the body further away from its original position. This is because the weight of the body acts downwards through G, while the buoyant force acts upwards through B. The difference in these forces creates a torque that causes the body to rotate away from its original orientation.
C. G and B are coincident:
If the center of gravity (G) and the center of buoyancy (B) are coincident, the body will be neutrally stable. When the body is displaced, there is no torque generated to rotate the body back to its original position. The body will remain in its displaced position without any tendency to return to its original orientation.
D. Independent of the locations of G and B:
This option is incorrect because the stability of a completely submerged body is dependent on the relative positions of G and B. The location of G above or below B determines whether the body is stable, unstable, or neutrally stable.
In conclusion, the correct answer is option A, where G is located below B. When G is below B, the body is stable and tends to return to its original position when displaced.
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