Given that $K=$ energy, $V=$ velocity, $T=$ time. If they are chosen as the fundamental units, then what is…

Given that $K=$ energy, $V=$ velocity, $T=$ time. If they are chosen as the fundamental units, then what is dimensional formula for surface tension?
  1. $\left[K V^{-2} \mathrm{~T}^{-2}\right]$
  2. $\left[K^2 V^2 T^{-2}\right]$
  3. $\left[K^2 V^{-2} T^{-2}\right]$
  4. $\left[K V^2 T^2\right]$

Solution

Surface tension $=\frac{F}{\ell}=\frac{F}{\ell} \cdot \frac{\ell}{\ell} \cdot \frac{T^2}{T^2}$ (As, $F . \ell=K\left(\right.$ energy) $; \frac{T^2}{\ell^2}=V^{-2}$ ) Therefore, surface tension $=\left[K V^{-2} T^{-2}\right]$

Asked in: JEE Main 2012 (07 May Online)

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