The density of ice `x cm^(-3)` and that of water is `y gcm^(-3)`. What is the change in volume when `mg` of ice melts?

Options

A. `m(y-x)`
B. `(y-x)/(m)`
C. `my(y-x)`
D. `(m)/(y)-(m)/(x)`

Explanation

To find the change in volume when `m` grams of ice melts, we can follow these steps:

### Step 1: Understand the problem
When `m` grams of ice melts, it transforms into `m` grams of water. We need to calculate the change in volume that occurs during this transformation.

### Step 2: Calculate the volume of ice
The volume of ice can be calculated using the formula:
\[ \text{Volume of ice} = \frac{\text{mass of ice}}{\text{density of ice}} = \frac{m}{x} \]
where `m` is the mass of the ice and `x` is the density of ice in grams per cubic centimeter.

### Step 3: Calculate the volume of water
Similarly, the volume of water formed from the melted ice can be calculated as:
\[ \text{Volume of water} = \frac{\text{mass of water}}{\text{density of water}} = \frac{m}{y} \]
where `y` is the density of water in grams per cubic centimeter.

### Step 4: Calculate the change in volume
The change in volume when the ice melts is given by the difference between the volume of water and the volume of ice:
\[ \text{Change in volume} = \text{Volume of water} - \text{Volume of ice} \]
Substituting the volumes calculated in Steps 2 and 3, we have:
\[ \text{Change in volume} = \frac{m}{y} - \frac{m}{x} \]

### Step 5: Factor out `m`
We can factor out `m` from the equation:
\[ \text{Change in volume} = m \left( \frac{1}{y} - \frac{1}{x} \right) \]

### Final Result
Thus, the change in volume when `m` grams of ice melts is:
\[ \text{Change in volume} = m \left( \frac{1}{y} - \frac{1}{x} \right) \]

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