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Question

(a)

Dimensions of

$\frac{v}{\sqrt{\sigma}}=\frac{[v]}{\sqrt{\rho \cdot h^3}}=\frac{\left[ T ^{-1}\right]}{\sqrt{\left[\rho R ^3\right]}}=\frac{\

Vedclass · Accepted Answer

$k \rho g R^2 / \sigma$

Vedclass · Answer

(a)

Dimensions of

$\frac{v}{\sqrt{\sigma}}=\frac{[v]}{\sqrt{\rho \cdot h^3}}=\frac{\left[ T ^{-1}\right]}{\sqrt{\left[\rho R ^3\right]}}=\frac{\left[ MT ^{-2}\right]}{\sqrt{\left[\frac{ M }{ L ^3} \cdot L ^3\right]}}$

$=\left[ M ^0 L ^0 T ^0\right]$

Now, from option $(a)$,

Dimensions of $\frac{k \rho g R^2}{\sigma}=\frac{\left[k \rho g R^2\right]}{[\sigma]}$

$=\frac{\left[\frac{ M }{ L ^3}\right] \cdot\left[ LT ^{-2}\right] \cdot\left[ L ^2\right]}{\left[ MT ^{-2}\right]}$

$=\left[ M ^0 L ^0 T ^0\right]$

So, by dimensional analysis, option $(a)$ is correct.

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