Question

Assertion :The dimensional formula of surface energy is $\left[M^1{L}^2{T}^{-2}\right]$ Reason: Surface energy has same dimensions as that of potential energy

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is D Both Assertion and Reason are incorrect

Surface energy is the energy per unit area of the surface.

Thus $S.E.=\frac{Energy}{Area}$

i.e. $S.E.=\frac{Workdone}{Area}$

So, dimensional formula is:

i.e. $S.E.=\frac{\left[M{L}^2{T}^{-2}\right]}{\left[L^2\right]}$

$S.E.=\left[M{L}^0{T}^{-2}\right]$

Also, Potential energy,

$P.E.=m\times g\times h$

Its dimensional formula is:

$P.E.=\left[M^1\right]\left[L^1{T}^{-2}\right]\left[L^1\right]$

$P.E.=\left[M^1{L}^2{T}^{-2}\right]$

It is clear that dimensional formula for surface energy given in assertions incorrect. Also, it is not matching with dimensional formula of potential energy.

Hence both assertion and reason are incorrect.

‘Thus option D is correct.