Question

In a system of units of force f acceleration and time are the dimensional formula of energy is

Answer 1

Answer:

Energy E ∝[F]a[A]b[T]c

Writing the dimensions on both sides, we have

[ML2T−2]=k[MLT−2]a[LT−2]b[T]c

[ML2T−2]=k[MaLa+bT−2a−2b+c]

Taking dimensional balance of equation into consideration and equating the dimensions of both sides, we get

a = 1 ..(i)

a + b = 2 ..(ii)

- 2a - 2b + c = - 2 ..(iii)

On solving Eqs. (i), (ii) and (iii), we get

a = 1, b = 1, c = 2

∴[E]=[FAT2]