First slide

Dimensions of physical quantities

Question

In the relation $y = r \sin (ω t - k x),$ the dimensional formula of $ω / k$ are

Moderate

A

$[M^{0} L^{0} T^{0}]$
B

$[M^{0} L^{1} T^{- 1}]$
C

$[M^{0} L^{0} T^{1}]$
D

$[M^{0} L^{1} T^{0}]$

Solution

Given, $y = r \sin (ω t - k x)$
where, $ω t = a n g l e$
$∴ ω = \frac{1}{T} = [T^{- 1}] (a n g l e i s \dim e n s i o n l e s s)$
Similarly kx = angle
$∴ k = \frac{1}{x} = [L^{- 1}]$
$\frac{ω}{k} = \frac{[T^{- 1}]}{[L^{- 1}]} = [L T^{- 1}]$

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