Question

A physical quantity $X$ depends on another physical quantities as $X=Y F e^{-\beta r^{2}}+Z W \sin (\alpha r)$ where $r, F$ and $W$ represents distance, force and work respectively and $Y$ and $Z$ are unknown physical quantities and $\alpha, \beta$ are positive constants.
If $Y$ represents velocity, then $\operatorname{dim}(X)$ is equal to

• A. $M L^{2} T^{23}$
• B. $M^{-1} L^{2} T^{-3}$
• C. $M L^{2} T^{2}$
• D. None of these

Answer 1

Answer: (A)

If $D(Y)=\left[L T^{-1}\right]$, then $D(X)=\left[L T^{-1} M L T^{-2}\right]$
$=\left[M L^{2} T^{-3}\right]$ from equation (i).