At what respective value of a, b, and c would the unit of work, the 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
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 1, b = 2, c = –2
The value of a, band c = 1, 2, –2
There is an explanation video available below.