Question

The velocity of a particle is given by v = ωAcos(ωt - kx), where x is position and t is time. The dimenstion of k/ω is 

Answer 1

Correct option is (2) [L^-1T¹]

Given equation is, \(v = \omega A \cos (\omega t - kx)\)

As we know, all trigonometric functions are dimensionless. Therefore, the term \(\cos (\omega t - kx)\) should be dimensionless.

⇒ \([\omega t - kx] = [M^0L^0T^0]\)

Two quantities can be subtracted if they have same dimensions.

Therefore, 

\([\omega t] = [kx] = [M^0L^0T^0]\)

Dimension of time \(t = [T]\)

⇒ \([\omega ] = \frac{[M^0L^0 T^0]}{[T]} = [T^{-1}]\)

Also, dimension of position \(x = [L]\)

⇒ \([k] = \frac{[M^0L^0T^0]}{[L]} = [L^{-1}]\)

Therefore, dimension of \(\frac kw\) is given by

\(\left[\frac k\omega\right] = \frac{[L^{-1}]}{[T^{-1}]} = [L^{-1}T^1]\)

Answer 2

We know that 

\(V = \frac\omega k\)

then

\(\frac k\omega =\frac1V\)

\(\frac k\omega =\frac1{[LT^{-1}]}\)

\(\frac k\omega =[L^{-1}T]\)