Question

Write the dimensions of $(a\times b)$ in the relation $E=\frac{b-x^2}{at}$, where $E$ is the energy, $x$ is the displacement and $t$ is time.

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

Answer 1

The correct option is B $\left[M^{-1}{L}^{2}T\right]$

Given relation is $E=\frac{b-x^2}{at}$,
so, here $b$ and $x^2$ should have same dimension i.e. $\left[b\right]=\left[L^2\right]$
Also, $\left[a\right]=\frac{[b-x^2]}{\left[E\right]\left[t\right]}$
$\Rightarrow \left[a\right]=\frac{\left[L^2\right]}{\left[M{L}^2{T}^{-2}\right]\left[T\right]}=\left[M^{-1}T\right]$
Thus, we have
$[a\times b]=\left[M^{-1}T\right]\left[L^2\right]=\left[M^{-1}{L}^{2}T\right]$