1. Tardigrade
  2. Question
  3. Physics
  4. A physical quantity X depends on another physical quantities as X=Y F e-β r2+Z W sin (α r) where r, F and W represents distance, force and work respectively and Y and Z are unknown physical quantities and α, β are positive constants. If Y represents velocity, then operatornamedim(X) is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. 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

Physical World, Units and Measurements

Solution:

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).