Assertion: The dimensional formula of surface energy is [ $M^{1} L^{2} T^{- 2}]$

Reason: Surface energy has same dimensions as that of potential energy

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Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

Assertion is correct but Reason is incorrect

Both Assertion and Reason are incorrect

answer is D.

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Detailed Solution

Concept: Surface energy is the energy per unit area of the surface

Thus  S . E = \frac{Energy}{Area}

Energy = work done
Therefore S.E =

\frac{Work Done}{Area}

So, dimensional formula is S.E =

\frac{[M^{1} L^{2} T^{- 2}]}{[L^{2}]}

Where M is mass, L is Length and T is Time
S.E = [

M L^{0} T^{- 2}]

Also, Potential energy
P.E = m × g × h
m stands for mass, g for gravitational acceleration, and h for height.
Its dimensional formula is
P.E = [

M^{1}

][

L^{1} T^{- 2}] [L^{1}]

M^{1} L^{2} T^{- 2}]

It is clear that the dimensional formula for surface energy given in the assertion is incorrect. Also, it is not matching with the dimensional formula of potential energy.
Hence, Both Assertion and Reason are incorrect.
Hence, the correct option is 4.

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