Question

In the equation $y=a \sin (\omega \mathrm{t}+\mathrm{kx}$, the dimensional formula of $\omega$ is

• A. $\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{-1}\right]$
• B. $\left[\mathrm{M}^{0} \mathrm{LT}^{-1}\right]$
• C. $\left[\mathrm{ML}^{0} \mathrm{~T}^{0}\right]$
• D. $\left[M^{0} L^{-1} T^{0}\right]$

Answer 1

Answer: (A)

$\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{-1}\right]$

Answer 2

The argument of a trigonometric function must be dimensionless. Therefore, the dimensions of $\omega$ must be such that when multiplied by time (which has dimension $[T]$), the result is dimensionless. Thus, the dimensional formula for $\omega$ is $[M^0L^0T^{-1}]$.