Multiple choice

When n fluids of masses $m_1,m_2...m_n$ and densities $p_1,p_2...p_n$ respectively are mixed together then resultant density of mixture is :

  1. $\dfrac{{\displaystyle\sum\limits_{i = 1}^n {{m_i}} }}{{\displaystyle\sum\limits_{i = 1}^n {{p_i}} }}$
  2. $\dfrac{{\displaystyle\sum\limits_{i = 1}^n {{m_i}{p_i}} }}{{\displaystyle\sum\limits_{i = 1}^n {{m_i}} }}$
  3. $\dfrac{{\displaystyle\sum\limits_{i = 1}^n {{m_i}} }}{{\displaystyle\sum\limits_{i = 1}^n {\dfrac{{{m_i}}}{{{p_i}}}} }}$

  4. infinity
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C Correct answer
Explanation

Density = Total Mass / Total Volume. Total mass = sum(m_i). Total volume = sum(m_i / p_i). Therefore, density = sum(m_i) / sum(m_i / p_i).

AI explanation

The resultant density of a mixture is calculated as total mass divided by total volume. The total mass is the sum of the individual masses, and the total volume is the sum of the individual volumes, where each volume is calculated as its mass divided by its density. Therefore, the resultant density is the sum of the masses divided by the sum of the ratios of mass to density for each fluid.

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