If \(21 g\) of alcohol of density \(0.7 gcm ^{-3}\) is mixed with \(10 g\) of water, what would be the density of the resulting mixture?
A. \(780 gcm ^{-3}\) B. \(0.78 gcm ^{-3}\) C. \(30 gcm ^{-3}\) D. \(10 gcm ^{-3}\)
Correct Answer: B
Explanation
Correlating equation \(\bar{\rho}=\frac{\text { mass of alcohol+mass of water }}{\text { vol.of alcohol+vol.of water }}\) vol. of alcohol \(=\frac{m}{\rho}=\frac{21}{0.7}=30 cm ^{3}\) vol. of water \(=\frac{10}{1}=10 cm ^{3}\) $$ \begin{aligned} \rho_{\text {mixture }}=\frac{21+10}{30+10} &=\frac{31}{40} . \\ &=0.78 g / cm ^{3} \end{aligned} $$
