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Upthrust and buoyancy

Buoyancy $$(\vecphy{B})$$ or upthrust is the force exerted by a fluid to oppose the weight of an object floating on or submerged in the fluid. This force is also called the buoyant force.

Archimedes' principle states that the buoyancy of an object immersed in a fluid (not touching the base of a container) is equal in magnitude to the weight of the fluid displaced by the object: $$$\begin{align*}B&=m_{\text{displaced fluid}}g\\&=\rho V_{\text{displaced fluid}}g\end{align*}$$$

A ship on the sea is pulled down by gravitational force (weight), but it is pushed upwards by the buoyant force. The more water the ship displaces, the stronger the buoyancy.

A body will sink or float depending on whether the upthrust is lower or higher than the weight. A body is in equilibrium when its weight is equal in magnitude to the upthrust.

$$P=$$fluid pressure; $$\rho=$$density of the fluid, $$g=$$magnitude of gravitational acceleration, $$h=$$depth of the point.