Question

Write the dimensions of $a \times b$ in the relation $E=\frac{b-x^{2}}{a t}$, 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. $M L\, T^{-2}$

Answer 1

Answer: (B)

Here, $b$ and $x^{2}=L^{2}$ have same dimensions.
Also, $a=\frac{L^{2}}{E \times t}=\frac{L^{2}}{\left(M L^{2} T^{-2}\right) T}=M^{-1}\, T^{1}$
$a \times b=\left[M^{-1} L^{2} T^{1}\right]$