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Standard XII

Physics

Dimensional Analysis

A wave functi...

Question

A wave function expressing the displacement (y) as a function of its position (x) ad time (t) is given as $Y = P$ $l o g (Q x + R t) .$
Which of the following expressions has dimensions different from other?

γ R

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P R

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\frac{R}{Q}

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Q R

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Solution

The correct option is C $Q R$
Given,

$γ = P l o g (Q x + R t)$

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,

$Y R = [L T^{- 1}]$

$P R = [L T^{- 1}]$

$\frac{R}{Q} = [L T^{- 1}]$

$Q R = [L^{- 1} T^{- 1}]$

So the dimension of $Q R$ is different from others.

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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?

The correct option is C QRGiven,γ=Plog(Qx+Rt)The same dimensions can be added, subtract and equate and exponents are dimensionless.Using above rule we getY=[L], P=[L], Q=[L−1], R=[T−1]Then,YR=[LT−1]PR=[LT−1]RQ=[LT−1]QR=[L−1T−1]So the dimension of QR is different from others.

A wave function expressing the displacement (y) as a function of its position (x) ad time (t) is given as $Y = P$ $l o g (Q x + R t) .$
Which of the following expressions has dimensions different from other?