question_answer

If energy (E), velocity [v] and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be [NEET 2015]

A) \[[E{{v}^{-2}}{{T}^{-1}}]\]

B) \[[E{{v}^{-1}}{{T}^{-2}}]\]  

C) \[[E{{v}^{-2}}{{T}^{-2}}]\]

D) \[[{{E}^{-2}}{{v}^{-1}}{{T}^{-3}}]\]

Correct Answer: C

Solution :

We know that

Surface tension \[(S)=\frac{\text{Force}\,[F]}{\text{Lenght}\,[L]}\]

So,

Energy (E) = Force  displacement

Velocity

A.s,

where, a, b, c are constants.

From the principle of homogeneity,

[LHS] = [RHS]

Equating the power on both sides, we get

So