Question

If kinetic energy '$K$', velocity '$v$' and time '$T$' are chosen as the fundamental units, the formula for surface tension $S$$=$
($A$ is a constant)

• A. $\frac{v^2{K}^2}{AK}$
• B. $\frac{v^2}{AKT}$
• C. $\frac{{AKT}^2}{v^2}$
• D. $\frac{AK}{v^2{T}^2}$

Answer 1

The correct option is D $\frac{AK}{v^2{T}^2}$

Let $K,v,T$ are fundamental units.Hence we want formula of surface tension in terms of $K,v,T$ .

Original formula for surface tension is $S=F/d$

$\therefore S=\frac{ma}{d}=\frac{mv}{dT},$ because $a=v/T$,

multiplying and divide given eq by $v$ and $2$ we get,

$S=2\times \frac{1}{2}\frac{m{v}^2}{dTv}=\frac{2K}{dTv}$ because $K=\frac{1}{2}m{v}^2,$

multiplying and divide given eq by $T$ we get,

$S=\frac{2K}{\frac{d}{T}{T}^{2}v}=\frac{2K}{v{T}^{2}v}$ because $v=d/T$,

taking $A=2$ we get,

$\therefore S=\frac{AK}{v^2{T}^2}$ .