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If energy (E), velocity (V) and time (T) are chosen as fundamental quantities, the dimensional formula of surface tension will be
A
$[EV^{-2}T^{-1}]$
B
$[EV^{-1}T^{-2}]$
C
$[EV^{-2}T^{-2}]$
D
$[E^{-2}V^{-1}T^{-3}]$
Detailed Solution
Let $\sigma = E^aV^bT^c$.
$[ML^0T^{-2}] = [ML^2T^{-2}]^a\,[LT^{-1}]^b\,[T]^c = [M^a L^{2a+b} T^{-2a-b+c}]$
Comparing powers: $a = 1$; $2a + b = 0 \Rightarrow b = -2$; $-2a - b + c = -2 \Rightarrow c = -2$.
So the dimensional formula of surface tension is $[EV^{-2}T^{-2}]$.
$[ML^0T^{-2}] = [ML^2T^{-2}]^a\,[LT^{-1}]^b\,[T]^c = [M^a L^{2a+b} T^{-2a-b+c}]$
Comparing powers: $a = 1$; $2a + b = 0 \Rightarrow b = -2$; $-2a - b + c = -2 \Rightarrow c = -2$.
So the dimensional formula of surface tension is $[EV^{-2}T^{-2}]$.