Physics

A wave function expressing the displacement (y) as a function of its position (x) ad time (t) is given as $$Y= P$$  $$ {log} (Qx + Rt).$$
Which of the following expressions has dimensions different from other?


ANSWER

$$QR$$


SOLUTION
Given,

$$\gamma=P\,log(Qx+Rt)$$

The same dimensions can be added, subtract and equate and exponents are dimensionless.

Using above rule we get
$$Y=[L]$$, $$P=[L]$$, $$Q=[L^{-1}]$$, $$R=[T^{-1}]$$

Then,

$$Y R=[LT^{-1}]$$

$$PR=[LT^{-1}]$$

$$\dfrac RQ=[LT^{-1}]$$

$$QR=[L^{-1}T^{-1}]$$

So the dimension of $$QR$$ is different from others.
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