At what respective value of a b and c would the unit of work (joule) be dimensionally similar to Ma Lb Tc?
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 = Ma Lb Tc
i.e. Ma Lb Tc = as a = 1, b = 2, c = –2
The value of a, b and c = 1, 2, –2