Question

State the principle of homogeneity of dimensions and check the below equation is dimensionally correct or not
V=u+at

Answer 1

It states that the dimensions of each term on both the sides of equation are same, then the physical quantity will be correct.

Explanation:

The principle of homogeneity is that the dimensions of each the terms of a dimensional equation on both sides are the same. any equation or formulae involving dimensions (like mass, length, time, temperature, electricity) have the terms with same dimensions.

            v=u+at

where u = initial velocity (m/s)

           v= final velocity (m/s)

            a = acceleration (m/$s^{2}$)

            t= time taken

L.h.s dimensions for v = [$M^{0}LT^{-1}$]

R.H.S  dimension of u =  [$M^{0}LT^{-1}$]

          dimension of at = [$M^{0}LT^{-1}$]

dimensions of v,u and at are same.

so the equation v=u+at is dimensionally correct