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Equal masses of two substances of densities \mathrm{\rho_1} and \mathrm{\rho_2} are mixed together. The density of the mixture would be

Option: 1

\mathrm{\frac{1}{2}\left(\rho_1+\rho_2\right)}


Option: 2

\mathrm{\sqrt{\rho_1 \rho_2}}


Option: 3

\mathrm{\frac{\rho_1 \rho_2}{\left(\rho_1+\rho_2\right)}}


Option: 4

\mathrm{\frac{2 \rho_1 \rho_2}{\left(\rho_1+\rho_2\right)}}


Answers (1)

The density of the mixture is

\mathrm{ \rho=\frac{\text { total mass }}{\text { total volume }}=\frac{m_1+m_2+m_3+\cdots+m_n}{\frac{m_1}{\rho_1}+\frac{m_2}{\rho_2}+\frac{m_3}{\rho_3}+\cdots+\frac{m_n}{\rho_n}} }
For two substances mixed together, we have

\mathrm{ \rho=\frac{m_1+m_2}{\frac{m_1}{\rho_1}+\frac{m_2}{\rho_2}}=\frac{\left(m_1+m_2\right) \rho_1 \rho_2}{\left(m_1 \rho_2+m_2 \rho_1\right)} }
Given \mathrm{m_1=m_2=m}. Therefore, \mathrm{\rho=\frac{2 \rho_1 \rho_2}{\left(\rho_2+\rho_1\right)}}.

Hence the correct choice is (d).

Posted by

Ramraj Saini

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