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 the time.

• A. $M{L}^{2}T$
• B. $M^{-1}{L}^2{T}^1$
• C. $M{L}^2{T}^{-2}$
• D. $ML{T}^{-2}$

Answer 1

The correct option is B $M^{-1}{L}^2{T}^1$

$E=\frac{b-x^2}{at}$ $E$ is energy $x$ is displacement $t$ time

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

$x=\left[L\right]$

$t=\left[T\right]$

$b$ will have unit same $x^2$

$b=\left[L^2\right]$

$a=\left[\frac{b-x^2}{Et}\right]=\frac{\left[L^2\right]}{[{ML}^2{T}^{-2}\times T]}=\left[M^{-1}T{L}^0\right]$

$a\times b=\left[L^2\right]\left[M^{-1}{L}^{0}T\right]$

$=\left[M^{-1}{L}^{2}T\right]$