A solid sphere of radius R and average mass density ρ1 is completely submerged in a tank filled with a liquid of mass density ρw with ρi > ρw- The sphere is held in place by string attached to the bottom of tank. The tension in the string is
Weight of sphere
The tension in the string, T, compensates the difference between the weight and the buoyant force and hence W = T + Fb
If B = Center of buoyancy, G = Center of gravity and M= Metacenter, of afloating body, the body will be in stable equilibrium if
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
A metal block is thrown into deep lake. As it sinks deeper in water, the buoyant force acting on it
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.
When a block of ice floating on water in a container melts, the level of water in the container
When a ship enters sea from a river one can expect it
A large metacentric height in a vessel
For warship, metacentric height of a ship should vary between
The metacentric height of a passenger ship is kept water lower than that of a naval or a cargo ship. This is because
The buoyant force is
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.
The metacenter is
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.