Question

find the dimensions of the constant a*b in the relation E=
$(b - {x}^{2} ) \div at \: \: where \: e \: is \: energy \: x \: is \: distance \: and \: t \: is \: time$

Answer 1

According to the principle of homogeneity of dimensions, [E] = [b] = [(x2/a) t]

[E] = [M L2 T−2]
Therefore [b] = [M L2 T−2]
Now  [E] = [(x2/a) t] = [L2 T /a]
              ⇒ [a] = [L2 T /E]
                       = [L2 T /(M L2 T−2)] 
                       = [ T3/M]
Therefore [a] = [M−1 T3]