If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy.
 If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy.

(1) [F][A][T]                            (2) [F][A][T2]

(3) [F][A][T–1]                        (4) [F][A–1][T]

Solution: Answer (2)

We know that,

[E] = [Fa][Ab][Tc]

=> [ML2T–2] = [MLT–2]a [LT–2]b [T]c

[ML2T–2] = [MaL a + b T–2a – 2b + c]

Comparing dimensions on both sides, we get:

a = 1; a + b = 2 and –2 = – 2a – 2b + c

b = 1 and c = 2

[E] = [FAT2]