In the relation y=a cos(wt-kx), the dimensional formula for k is

Asked by Anil | 10th May, 2017, 08:54: PM

Expert Answer:

The dimensional formula for 'k' can be obtained in two ways.
First method:
As (ωt - kx) is an angle, it has to be dimensionless. So, kx should be dimensionless.
Hence, the dimensions of k = 1/dimensions of x
 
Therefore, [k] = L-1
 
Second method: Dimension of ωt = dimension of kx
begin mathsize 12px style therefore straight k equals ωt over straight x equals fraction numerator straight T to the power of negative 1 end exponent straight T over denominator straight L end fraction equals straight L to the power of negative 1 end exponent end style

Answered by Romal Bhansali | 11th May, 2017, 02:39: PM