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  4. The dimensions of physical quantity X in the equation force =(X/√ text Density ) is given by :

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Q. The dimensions of physical quantity $X$ in the equation force $=\frac{X}{\sqrt{\text { Density }}}$ is given by :

Physical World, Units and Measurements

Solution:

$\begin{aligned} \text { }[\mathrm{X}] &=[\mathrm{F}] \times[\rho]^{1 / 2} \\ &=\left[\mathrm{MLT}^{-2}\right] \times\left[\frac{\mathrm{M}}{\mathrm{L}^{3}}\right]^{1 / 2}=\left[\mathrm{M}^{3 / 2} \mathrm{~L}^{-1 / 2} \mathrm{~T}^{-2}\right] \end{aligned}$