Question

If the buoyant force $F$ acting on an object depends on its volume $V$ immersed in a liquid, the density $\rho$ of the liquid and the acceleration due to gravity $g$. The correct expression for $F$ can be

• A. $V\rho g$
• B. $\frac{\rho g}{V}$
• C. $\rho g{V}^2$
• D. $\sqrt{\rho gV}$

Answer 1

Answer: (A)

$F\propto V^a{\rho }^b{g}^c$
$F={\left[L^3\right]}^a{\left[M{L}^{-3}\right]}^b{\left[L{T}^{-2}\right]}^c$
$\left[ML{T}^{-2}\right]=F=\left[M^b{L}^{3s-3b+c}{T}^{-2c}\right]$
On comparing,
$b=1,-2c=-2$
$\Rightarrow c=1$
$3a-3b+c=1$
$\Rightarrow 3a-3+1=1$
$\Rightarrow 3a-2=1$
$\Rightarrow 3a=3$
$\Rightarrow 3a=1$
So, on putting all these values,
$F=V\rho g$