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EEJ MAIN Physics QUESTION #7039
Question 1
In SI units, a material's density is $128 \text{ kg m}^{-3}$. Calculate its numerical value in a system where the unit of length is $25 \text{ cm}$ and the unit of mass is $50 \text{ g}$.
  • $40$✔️
  • $16$
  • $640$
  • $410$
Correct Answer Explanation

Using $n_1 u_1 = n_2 u_2$:

$128 \times [\text{kg} \cdot \text{m}^{-3}] = n_2 \times [(50 \text{ g}) \cdot (25 \text{ cm})^{-3}]$

$n_2 = 128 \times \left( \frac{1000 \text{ g}}{50 \text{ g}} \right) \times \left( \frac{25 \text{ cm}}{100 \text{ cm}} \right)^3$

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