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Explaining buoyancy

Buoyancy is the force exerted by a fluid on an object opposing the weight of the object.

The origin of buoyancy is the difference in pressure at different depths. The depth influences the pressure at a given point of an object according to $$P=\rho gh$$.

The top and bottom of a submerged sphere (located at $$h_1$$ and $$h_2$$ respectively) will be subject to different pressures: $$$ \begin{align*}P_1=\rho gh_1 \quad& \quad P_2=\rho gh_2\\ h_{1}&\lt h_{2}\\\therefore P_{1}&\lt P_{2}\end{align*}$$$

This difference in pressure results in an upward force on the ball, known as the buoyant force.

The upthrust is due to the difference in pressure at different heights.
The upthrust is due to the difference in pressure at different heights.