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Question
Taking force, length and time to be the fundamental quantities, find the dimensions of density .
Solution
Density
\[= \frac{m}{v} = \frac{\left( \text{ force/acceleration } \right)}{\text{ volume}}\]
\[ \left[\text{ Acceleration }\right] = \left[ {LT}^{- 2} \right] \text{ and [volume] } ={\left[ L^3 \right]}$\]
\[ \therefore \text{ [Density]} = \frac{\left[ F/ {LT}^{- 2} \right]}{\left[ L^3 \right]} = \frac{F}{L^4 T^{- 2}} = \left[ {FL}^{- 4} T^2 \right]\]
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