A drop of water of mass `m` and density `rho` is placed between two weill cleaned glass plates, the distance between which is `d`. What is the force of attraction between the plates?
`(T=` surface tension)

Options

A. `(Tm)/(2 rho d^(2))`
B. `(4Tm)/(rho d^(2))`
C. `(2Tm)/(rho d^(2))`
D. `(Tm)/(rho d^(2))`

Answer

To find the force of attraction between two glass plates with a drop of water placed between them, we can follow these steps:

### Step 1: Understand the Problem
We have a drop of water with mass \( m \) and density \( \rho \) placed between two glass plates that are separated by a distance \( d \). We need to find the force of attraction between these plates due to the surface tension \( T \) of the water drop.

### Step 2: Identify the Relevant Formula
The force of attraction \( F \) between two surfaces due to surface tension can be expressed as:
\[ F = T \cdot L \]
where \( T \) is the surface tension and \( L \) is the length of the contact line between the liquid and the surfaces.

### Step 3: Consider the Two Surfaces
Since the drop of water is in contact with both glass plates, the total force of attraction will be:
\[ F = 2 \cdot T \cdot L \]
This factor of 2 accounts for the interaction with both surfaces.

### Step 4: Determine the Length \( L \)
The length \( L \) can be related to the area \( A \) of the drop. The area can be expressed in terms of the mass \( m \) and density \( \rho \) of the water drop:
\[ A = \frac{m}{\rho \cdot d} \]
where \( d \) is the distance between the plates.

### Step 5: Substitute \( L \) into the Force Equation
Now substituting \( L \) into the force equation:
\[ F = 2 \cdot T \cdot \left(\frac{m}{\rho \cdot d}\right) \]
This simplifies to:
\[ F = \frac{2Tm}{\rho d} \]

### Step 6: Final Expression for Force
Thus, the final expression for the force of attraction between the plates is:
\[ F = \frac{2Tm}{\rho d^2} \]

### Conclusion
The force of attraction between the plates is given by:
\[ F = \frac{2Tm}{\rho d^2} \]