Test: Buoyancy & Floatation - 1 - Mechanical Engineering

Weight of sphere

Buoyant force,

since

The tension in the string, T, compensates the difference between the weight and the buoyant force and hence W = T + F_b

so,

For a floating body
Metacentre above centre of gravity→ Stable Equilibrium
Metacentre coincides centre of gravity→ Neutral Equilibrium
Metacentre below centre of gravity→ Unstable Equilibrium
For a submerged body
Centre of buoyancy above centre of gravity→ Stable Equilibrium
Centre of buoyancy coincides centre of gravity→ Neutral Equilibrium
Centre of buoyancy below centre of gravity→ Unstable Equilibrium

Buoyant force equals the weight of water which has been displaced by an object.
Since, irrespective of the metal block position, the volume displaced by metal is same, hence, buoyant force remains the same.

A body submerged in a fluid experiences an upward thrust due to fluid pressure. This force is called buoyant force and a body immersed in a fluid is buoyed or lifted up a force equal to the weight of the fluid displaced by the body. The body apparently loses as much of its weight as the weight of the fluid displaced by it.

Metacenter is the point of inter section of normal axis of the body with the new line of action of buoyant force when body is tilted.