Question

A right circular cylinder has a mass $m$, radius $r$, and a height $h$. The cylinder is completely submerged in a fluid of density $\rho$ as shown in the diagram and is released. What is the magnitude of the net force on the cylinder initially?

• A. $r\rho gh+mg$
• B. $|r\rho gh-mg|$
• C. $\pi r^2\rho gh+mg$
• D. $\left|mg-\pi r^{2}h\rho g\right|$

Answer 1

The correct option is D $\left|mg-\pi r^{2}h\rho g\right|$

Archimedes' principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces. Archimedes' principle is a law of physics fundamental to fluid mechanics.

Net force $=|mg-\text{volume}\ast \text{density of fluid}\ast g|=|mg-\pi r^{2}h\ast \rho g|=|mg-\pi r^{2}h\rho g|$

Hence option 'D' is correct.