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Why length, mass and time are chosen as base quantities in mechanics?

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Because these are the fundamental quantities of basic physical quantities .These are treated as independent quantities are not usually defined in terms of other physical quantities .
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Coz they are the most basic units and not related to each other and also all other quantities can be expressed in terms of L,T n M
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Because these all three are fundamental quantities....All other physical quantities are derived from these quantities
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