Question

The density of ice is \[x\;gm/cc\;\] and that of water is \[y\;gm/cc\]. What is the change in volume in \[cc\], when \[m\;gm\;\] of ice melts?
A. \[m\left( {y - x} \right)\]
B. \[\left( {y - x} \right)/m\]
C. \[mxy\left( {x - y} \right)\]
D. \[m\left( {1/y - 1/x} \right)\]

Answer 1

Hint:Here, we are given that some amount of ice is melting. We know that when ice melts, it converts into water. Because of this, the volume of ice decreases and the volume of water increases. By using this point, we will apply the definition of density to find our answer.

Formula used:
$\rho = \dfrac{m}{V}$,
where, $\rho $ is the density, $m$ is the mass, $V$ is the volume.

Complete step by step answer:
We are given that \[m\;gm\;\] of ice melts.
We know that the density of ice is \[x\;gm/cc\;\]and as ice melts its volume decreases.
We have the formula for density
$
\rho = \dfrac{m}{V} \\
\Rightarrow V = \dfrac{m}{\rho } \\ $
Thus, the reduction in the volume of ice is given by $\dfrac{m}{x}cc$. Now, as the ice melts the volume of water increases as ice is converted into water after melting. We are given that the density of the water is \[y\;gm/cc\]. Therefore, the increase in the volume of the water is given by $\dfrac{m}{y}cc$. The total change in volume will be equal to the subtraction of the increase in the volume of the water and decrease in the volume of the ice.
Therefore, the change in volume $ = \dfrac{m}{y} - \dfrac{m}{x} = m\left( {\dfrac{1}{y} - \dfrac{1}{x}} \right)cc$

Thus, option D is the right answer.

Note:To solve this question we have used the concept of density. Density can be defined as the ratio of mass to the volume. For example, here we have determined the decrease in volume of ice and increase in volume of water by using the formula of density.