First slide

Physical quantities and units

Question

The density of a material in CGS system of units is 4 g/cc. In a system of units in which unit of length is 2 cm and unit of mass is 16 g, the numerical value of density of material is: _____________ units.

Easy

Solution

$\begin{array}{l} [density] = [M L^{- 3}] \\ ∴ n_{2} = n_{1} (\frac{M_{1}}{M_{2}}) {(\frac{L_{1}}{L_{2}})}^{- 3} \\ \Rightarrow n_{2} = (4) (\frac{1 g}{16 g}) {(\frac{1 cm}{2 cm})}^{- 3} = 4 (\frac{1}{16}) (8) = 2 \end{array}$

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