Question

Given that $K =$ energy, $V =$ velocity, $T =$ time. If they are chosen as the fundamental units, then what is dimensional formula for surface tension?

• A. $[KV^{-2}T^{-2}]$
• B. $[K^{2}V^2T^{-2}]$
• C. $[K^{2}V^{-2}T^{-2}]$
• D. $[KV^2T^{2}]$

Answer 1

Answer: (A)

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