Question

The velocity of a particle is given by \( v=A \omega \cos (\omega t-k x) \), where \( x \) is position and \( t \) is time. The dimension of \( \frac{k}{\omega} \) will be (1) \( \left[ M ^{0} L ^{-1} T \right] \) (2) \( \left[ M ^{0} L ^{-1}\right] \) (3) \( \left[ M ^{0} L ^{0} T ^{0}\right] \) (4) \( \left[ ML ^{-1} T \right] \)

Answer 1

Correct option is (1)

We know that v = w/k

\(\frac{1}{v}=\frac{k}{w}\)

\(\frac{k}{w}=\frac{1}{[LT^1]}\)

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