Question

the velocity of a particle is given by v=wAcos(wt-kx), where x is position and t is time. the dimensions of k/w is ........ 1. [LT^-1] 2. [L^-1T^1] 3. [L^2T^-2] 4. [L^-2T^2]

Answer 1

Given :

⟶ The velocity of a particle is given by

• v = Aω cos(ωt - kx)

where, x is position and t is time.

To Find :

➾ The dimensions of k/ω.

SoluTion :

✴ Dimension Formula :

$\mapsto\bf\:Position(x)=[L^1]$

$\mapsto\bf\:Time(t)=[T^1]$

➠ Only like quantities having the same dimensions can be added to or substracted from each other.

$\leadsto\sf\:[\omega][ t]=[k][x]$

$\leadsto\sf\:\dfrac{[k]}{[\omega]}=\dfrac{[t]}{[x]}$

$\leadsto\sf\:\dfrac{[k]}{[\omega]}=\dfrac{[T^1]}{[L^1]}$

$\leadsto\boxed{\bf{\dfrac{[k]}{[\omega]}=[L^{-1}T^1]}}$

Answer 2

Answer:

ACOS= dimensionless quantity.

by calculating V=wt and

V= Kt we get the dimensions