Question 2

The density of a material in SI units is 128 kg m$$^{-3}$$. In certain units in which the unit of length is 25 cm and the unit of mass is 50g, the numerical value of density of the material is:

$$[\rho] = \text{M}^1\text{L}^{-3}$$

$$n_2 = n_1 \left[\frac{\text{M}_1}{\text{M}_2}\right]^1 \left[\frac{\text{L}_1}{\text{L}_2}\right]^{-3}$$

$$n_2 = 128 \left[\frac{1\text{ kg}}{0.05\text{ kg}}\right]^1 \left[\frac{1\text{ m}}{0.25\text{ m}}\right]^{-3}$$

$$n_2 = 128 \times (20) \times (4)^{-3} = 128 \times 20 \times \frac{1}{64} = 2 \times 20 = 40$$

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