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?

$QR$

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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Single Correct Medium Published on 18th 08, 2020
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