Multiple choice

Equal masses of two substances of densities $\rho_A$ and $\rho_B$ are mixed together. The density of the mixture would be

  1. $\sqrt{\rho_A \rho_B}$
  2. $\frac{\rho_A + \rho_B}{2}$
  3. $\frac{\rho_A \rho_B}{\rho_A + \rho_B}$
  4. $\frac{2\rho_A \rho_B}{\rho_A + \rho_B}$
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D Correct answer
Explanation

The density of a mixture is the total mass divided by the total volume. With equal masses m, the total mass is 2m and the total volume is m/rho_A + m/rho_B, which simplifies to 2*rho_A*rho_B / (rho_A + rho_B).

AI explanation

Using the mixture density formula where total mass is divided by total volume, let the equal mass of each substance be $m$. The total mass becomes $2m$, and the total volume is $(m/ ho_A) + (m/ ho_B)$. This yields a density of $2m / (m/ ho_A + m/ ho_B)$, which simplifies to $2 ho_A ho_B / ( ho_A + ho_B)$.

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