Question

Given that $r=m^{2}sin\left(\pi \omega t\right)$, where $t$ represents time. If the unit of $m$ is N, then the unit of $\omega$ is :

• A. $T^{-1}$
• B. $N^2$
• C. $NS$
• D. Dimensionless

Answer 1

The correct option is A $T^{-1}$

Any trigonometric functions are the ratio of length so they are dimensionless. Thus, $sin\pi wt$ will dimensionless. Hence the term $wt$ will also be dimensionless. Thus the dimension of $w$ should be inverse of time $t$. So, $\left[w\right]=\left[T^{-1}\right]$