Q126 / 150 · MHT CET 2020 (15 Oct Shift 1) · Physics

Force $\mathrm{F}=\mathrm{P} \cos (\mathrm{Ax})+\mathrm{Q} \operatorname{Sin}(\mathrm{Bt})$ where $\mathrm{x}$ and $\mathrm{t}$ are displacement and time respectively. Which one of the following physical quantity has the dimensions of $\left[\frac{\mathrm{B}}{\mathrm{A}}\right] ?$

  • A
    velocity gradient
  • Correct answer
    B
    velocity
  • C
    angular velocity
  • D
    angular momentum

Solution

$F=P \cos (A x)+\varphi \sin (B t)$ ${Bt}=\text{no unit}$ ${Ax}=\text{no unit}$ $[B]=\left[T^{-1}\right]$ $[A]=\left[L^{-1}\right]$ $\left[\frac{B}{A}\right]=\left[L T^{-1}\right]$ $\quad \downarrow$ velocity dimensions.

Hence, the correct answer is option: 'B'.

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