Question

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

• A.
  $\left[F\right]\left[A^{-1}\right]\left[T\right]$
• B.
  $\left[F\right]\left[A\right]\left[T\right]$
• C.
  $\left[F\right]\left[A\right]\left[T^2\right]$
• D.
  $\left[F\right]\left[A\right]\left[T^{-1}\right]$

Answer 1

The correct option is C

$\left[F\right]\left[A\right]\left[T^2\right]$
Energy. $E\propto F^a{A}^b{T}^c$

$\left[E\right]=\left[F^a\right]\left(A^b\right)\left[T^c\right]$

$\Rightarrow \left[M{L}^2{T}^{-2}\right]=\left[ML{T}^{-2}{]}^a\right[L{T}^{-2}{]}^b[T{]}^c$

$\Rightarrow \left[M{L}^2{T}^{-2}\right]=\left[M^a{L}^{a+b}{T}^{-2a-2b+c}\right]$

Comparing dimensions on both sides.

$\Rightarrow a=1;a+b=2$ and

$-2=-2a-2b+c$

$\Rightarrow b=1$

$\Rightarrow -2=-2-2+c$

$\Rightarrow c=2$

$\left[E\right]=\left[FA{T}^2\right]$

Hence, $\left(C\right)$ is the correct answer.