If buoyant force F acting on an object depends on its volume V immersed in a liquid, density ρ of l

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1.Units, Dimensions and Measurement

medium

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

$\sqrt{\rho g V}$

Solution

(a)

$F \propto V^a \rho^b g^c$

$F=\left[L^3\right]^a\left[ ML ^{-3}\right]^b\left[ LT ^{-2}\right]^c$

$\left[ ML ^{-2}\right]=F=\left[ M ^{ b } L ^{3 a -3 b +c} T ^{-2 c}\right]$

On comparing.

$b=1,$

$-2 c=-2$

$\Rightarrow c=1$

$3 a-3 b+c=1$

$\Rightarrow 3 a-3+1=1$

$\Rightarrow 3 a-2=1$

$\Rightarrow 3 a=3 \Rightarrow a=1$

So, on putting all these values,

$F=V \rho g$

Standard 11

Physics

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