Question

In the relation y = a cos (wt - kx), the dimensional formula for k is
(1) [MºL-ST-1
(2) [MOLT')
(3) [M°L-'T)
(4) [MºLT)​

Answer 1

Answer:

$M^{0} L^{-1} T^{0}$

Explanation:

Y = a cos(wt - k x)

Since the dimension of Y, a and  Cos are dimensionless

Also , w = 1 ÷ t

So therefore

0 =  [ (1 ÷ t)(t) - k x]

0 = 1 - k x

1 = k x

K = 1 ÷ X (As x is for distance and its dimension is L )

K = 1 ÷ L

$K = L^{-1}$

Answer 2

Given:

$y = a \cos( \omega t - kx)$

To find:

Dimensions of k ?

Calculation:

We know that:

• The angles in trigonometric functions are dimensionless.

• Also, quantities with similar dimensions can be added.

• So, both $\omega t$ and kx are dimensionless.

$[kx] = [{M}^{0}{ L }^{0} {T}^{0} ]$

$\implies [kL] = [{M}^{0}{ L }^{0} {T}^{0} ]$

$\implies [k] = [{M}^{0}{ L }^{ - 1} {T}^{0} ]$

So, the dimension of [k] is :

$\boxed{ \bf [k] = [{M}^{0}{ L }^{ - 1} {T}^{0} ]}$