Q. Density of ice is $\rho$ and that of water is $\sigma$. What will be the decrease in volume when a mass $M$ of ice melts
A) $\frac{M}{\sigma - \rho}$
B) $\frac{\sigma - \rho}{M}$
C) $M\left\lbrack \frac{1}{\rho} - \frac{1}{\sigma} \right\rbrack$
D) $\frac{1}{M}\left\lbrack \frac{1}{\rho} - \frac{1}{\sigma} \right\rbrack$
Explanation
(c) Volume of ice $= \frac{M}{\rho}$, volume of water $= \frac{M}{\sigma}$
$\therefore$ Change in volume $= \frac{M}{\rho} - \frac{M}{\sigma} = M\left( \frac{1}{\rho} - \frac{1}{\sigma} \right)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.