Question

Does work and energy have same dimensional formula

Answer 1

work is the dot product of force and displacement along force.
e.g., $W=\vec{F}.\vec{S}$
dimension of force = $[MLT^{-2}]$
dimension of displacement = [L]
so, dimension of work = $[ML^2T^{-2}]$

now, energy , basically, there are two types of energy are most important , we should know
kinetic energy and potential energy.
kinetic energy = 1/2 mv² dimension [ML²T^-2]
and potential energy = mgh dimension [ML²T^-2]
so, dimension of energy = $[ML^2T^{-2}]$

here we can see of work and energy have same dimensional formula.

Answer 2

Answer:

Yes work and energy has same dimensional formula because energy is the capacity to do work so both have same dimensions.