Density of ice is `rho` and that of water is `sigma`. What will be the decrease in volume whebn a mass `M` of ice melts?

Options

A. `(M)/(sigma-rho)`
B. (sigma-rho)/(M)`
C. `M[(1)/(rho)-1/(sigma)]`
D. `1/M[(1)/(rho)-1/(sigma)]`

Explanation

To solve the problem of finding the decrease in volume when a mass \( M \) of ice melts, we can follow these steps:

### Step 1: Calculate the Volume of Ice
The volume of ice can be calculated using the formula:

\[ V_{\text{ice}} = \frac{M}{\rho} \]

where \( M \) is the mass of the ice and \( \rho \) is the density of ice.

### Step 2: Calculate the Volume of Water Produced
When the ice melts, it turns into water. The volume of water produced from the melted ice can be calculated as:

\[ V_{\text{water}} = \frac{M}{\sigma} \]

where \( \sigma \) is the density of water.

### Step 3: Find the Decrease in Volume
The decrease in volume when the ice melts can be found by subtracting the volume of water from the volume of ice:

\[ \Delta V = V_{\text{ice}} - V_{\text{water}} \]

Substituting the volumes we calculated in Steps 1 and 2:

\[ \Delta V = \frac{M}{\rho} - \frac{M}{\sigma} \]

### Step 4: Simplify the Expression
We can factor out \( M \) from the equation:

\[ \Delta V = M \left( \frac{1}{\rho} - \frac{1}{\sigma} \right) \]

This gives us the final expression for the decrease in volume when a mass \( M \) of ice melts.

### Final Answer
The decrease in volume when a mass \( M \) of ice melts is:

\[ \Delta V = M \left( \frac{1}{\rho} - \frac{1}{\sigma} \right) \]