Question

a wave function expressing displacement (y) as a function of its (x) and time (t) is given as y = P log (Qx + Rt)

Which of the following expressions has dimensions different from one another?

(1) yR

(2) PR

(3) R/Q

(4) QR

Answer 1

and your thinking is?

Answer 2

4.QR
Because log(x) is dimensionless. Here (x)=(Qx+Rt) So [Q][x]=[M^0][L^0][T^0] So [Q]=[L^-1]
Then [R]=[T^-1] & [P]=[L] ( Same as dimension of y= displacement)
Then the only answer is QR which have different dimension from the other three options.

Answer 3

Very bad

Answer 4

I didn't understand

Answer 5

Not understandable

Answer 6

Y=Plog(Qx+e^-Rt)
In log(x) x is dimensionless being a constant
So (Qx+e^-Rt) = 1
Also dimensions of Qx= dimensions of e^-Rt as only similar quantities can be added or subtracted
Hence Qx=1
Q= x^-1=[L^-1]
Similarly, -Rt = 1
R= [T^-1]
Y=p=[L]
Put these values in the options and find the odd one out i.e. QR