Question

A body of volume $V$ and density $\rho$ is kept completely immersed in a liquid of density ${\rho }_L$. If $g$ is the acceleration due to gravity, write expression for the following:

The upthrust on the body

• A. $V{\rho }_{L}g$
• B. $\frac{V}{{\rho }_{L}g}$
• C. $\frac{V{\rho }_L}{g}$
• D. None of the above

Answer 1

The correct option is A $V{\rho }_{L}g$

According to Archimedes' principle, any body completely or partially submerged in a fluid at rest is acted upon by an upward or buoyant force whose magnitude is equal to the weight of the fluid displaced by the body.

$F_B={\rho }_{L}Vg$ = Upthrust on the body

Here, $V=$ volume of submerged object,

${\rho }_L=$ density of fluid

$g=$ acceleration due to gravity