Question

If p=cos(kx - t), where p is pressure,x is
distance and t is time, then dimension of k is
(1) [ML-1T-1]
(2) [ML-2T-2]
(3) [M-1L3T3]
(4) [ML-2T-4]
​

Answer 1

Given : p=cos(kx - t) p is pressure,x is  distance and t is time,

To Find : Dimension of k

Solution :

kx - t   is linear addition / subtraction

Hence Dimension of kx & t would be Same

k . L  = T

=> k = T L⁻¹

no option Matches with the result  

Correct Question should be

p = B cos (kx-at)  

dimension of Bk will be

cos (kx-at)  is unit less

hence unit of pressure and B are Same

Pressure =  Force / Area  = M L⁻¹T⁻²

Dimension of  k = T L⁻¹

dimension of Bk =  M L⁻¹T⁻² T L⁻¹

= M L⁻²T⁻¹

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