If the units of length, mass and force are chosen as fundamental units, the dimensions of time would be

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If the units of length, mass and force are chosen as fundamental units, the dimensions of time would be

PhysicsUnits and DimensionsAIIMSAIIMS 2014

Options:

A $\left[\mathrm{M}^{1 / 2} \mathrm{~L}^{-1 / 2} \mathrm{~F}^{1 / 2}\right]$
B $\left[\mathrm{M}^{1 / 2} \mathrm{~L}^{1 / 2} \mathrm{~F}^{1 / 2}\right]$
C $\left[\mathrm{M}^{1 / 2} \mathrm{~L}^{1 / 2} \mathrm{~F}^{-1 / 2}\right]$
D $\left[\mathrm{M}^{1 / 2} \mathrm{~L}^{-1 / 2} \mathrm{~F}^{-1 / 2}\right]$

Solution:

1675 Upvotes Verified Answer

The correct answer is: $\left[\mathrm{M}^{1 / 2} \mathrm{~L}^{1 / 2} \mathrm{~F}^{-1 / 2}\right]$

$\begin{aligned} \text { As } F=\left[\mathrm{MLT}^{-2}\right] \text { or } & {\left[\mathrm{T}^2\right]=\frac{[\mathrm{ML}]}{[\mathrm{F}]} } \\ \text { or }[\mathrm{T}] & =\left[\mathrm{M}^{1 / 2} \mathrm{~L}^{1 / 2} \mathrm{~F}^{-1 / 2}\right]\end{aligned}$

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