Question

If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, then dimensional formula of surface tension will be :

• A. [E^-2 V^-1 T^-3]
• B. [E V^-2 T^-1]
• C. [EV^-1T^-2]
• D. [EV^-2T^-2]

Answer 1

The correct option is D

[EV^-2T^-2]

[Surface Tension] = $M{T}^{-2}$

$\therefore M{T}^{-2}=K{E}^a{V}^b{T}^c$

$=k\left(M{L}^2{T}^2{)}^a\right(L{T}^1)b{T}^c$
$M{T}^{-2}=K{M}^a{L}^{2a+b}{T}^{-2a-b+c}$
$\therefore a=1$

2a + b = 0

-2a – b + c = -2

On solving a = 1, b = -2 , c = - 2

$\therefore$ Required answer is $E{V}^{-2}{T}^{-2}$