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

At what respective value of a b and c would the unit of work (joule) be dimensionally similar to M^a L^b T^c?

A. 1, – 2, 1
B. 1, 2, – 2
C. 1, 1, –2
D. 2, 2, 1

Correct Answer:

Option B – 1, 2, – 2

Explanation

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 = M^a L^b T^c

i.e. M^a L^b T^c = as a = 1, b = 2, c = –2

The value of a, b and c = 1, 2, –2