In equation y=x^2 cos ^2 2 pi frac{beta gamma | vedclass

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Question

(a)
$y=x^2 \cos ^2 2 \pi\left(\frac{\beta \gamma}{\alpha}\right)$
The argument of a trigonometric ratio is always dimensionless.
$\frac{\beta \gamm

Vedclass · Accepted Answer

$m ^2, ms ^{-2}$

Vedclass · Answer

(a)
$y=x^2 \cos ^2 2 \pi\left(\frac{\beta \gamma}{\alpha}ight)$
The argument of a trigonometric ratio is always dimensionless.
$\frac{\beta \gamma}{\alpha}=\left[ M ^0 L ^0 T ^0ight] 	ext { or } \beta \gamma=\alpha \Rightarrow \gamma=\frac{ T }{ L ^2}$
$	ext { and } y=x^2 \Rightarrow\left[ L ^2ight]$
$\alpha= s ^{-1} \Rightarrow\left[ T ^{-1}ight], \beta=\left[ LT ^{-1}ight]^{-1} \Rightarrow\left[ L ^{-1} T ight]$
$y=m^2$
$\gamma= ms ^{-2}$

In equation $y=x^2 \cos ^2 2 \pi \frac{\beta \gamma}{\alpha}$, the units of $x, \alpha, \beta$ are $m , s ^{-1}$ and $\left( ms ^{-1}\right)^{-1}$ respectively. The units of $y$ and $\gamma$ are

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