If energy ( E ) , velocity ( V ) and time ( T ) are chosen as the fundamental quantities, the dimensional formula of surface tension will be___(For surface tension, Force=Surface tension × length)

Step-by-step solution

Dimensional formula of surface tension, S = M 1 L 0 T - 2 Dimensional formula of energy, E = M 1 L 2 T - 2 Dimensional formula of velocity, V = M 0 L 1 T - 1 By applying dimensional analysis, S = E a V b T c M 1 L 0 T - 2 = M 1 L 2 T - 2 a M 0 L 1 T - 1 b T c M 1 L 0 T - 2 = M a L 2 a + b T - 2 a - b + c On comparing, a = 1 2 a + b = 0 ⇒ b =   - 2 - 2 a - b + c = - 2 ⇒ c =   - 2 ∴ S = E 1 V - 2 T - 2