Question

Example 2.15 Let us consider an equation
-mu? = mgh
where m is the mass of the body, v its
velocity, g is the acceleration due to
gravity and his the height. Check
whether this equation is dimensionally
correct
Insider The dimensions of LHS are​

Answer 1

The principle of homogeneity is that the dimensions of each the terms of a dimensional equation on both sides are the same.

Explanation:

 The equation is mv-mu=mgh

m = mass of the body

v= velocity

g= acceleration due to gravity.

h= height

L.H.S  mv = $[M^{1}LT^{-1}$]

           mu =[ $M^{1} LT^{-1}$]

           mgh = [M][ $LT^{-2}$] {L]

so dimension sof L.H.S  is not equal to R.H.S

this equation is dimensionally incorrect