At what respective value of a, b, and c would the unit of work, the joule, be dimensionally similar to Ma Lb Tc?

At what respective value of a, b, and c would the unit of work, the joule, be dimensionally similar to Ma Lb Tc?

Answer Details

Work (w) = Force (f) × Distance (d)

Note: f = ma = mass × acceleration

= mass ×acceleration ×distance

= kg ×ms–2 × m

= kg m2 5–2

(Note: the dimension of kg = M, M = L & S = T)

Work = ML2 T–2 = Ma Lb Tc

i.e. Ma Lb Tc = as 1, b = 2, c = –2

The value of a, band c = 1, 2, –2