A rectangular frame having dimensions `"8 cm "xx " 4 cm "` and width of 3 mm is initially placed with its largest face flat on water surface. Calculate the downward force acting on the frame due to surface tension of water `("Surface tension of water "= 7.2 xx 10^(-4)"Ncm"^(-1))`

Answer

To solve the problem of calculating the downward force acting on the rectangular frame due to the surface tension of water, we can follow these steps:

### Step 1: Identify the dimensions of the frame
The dimensions of the rectangular frame are given as:
- Length (L) = 8 cm
- Breadth (B) = 4 cm
- Width (thickness) = 3 mm (which is 0.3 cm)

### Step 2: Calculate the perimeter of the largest face
Since the frame is placed with its largest face flat on the water surface, we need to calculate the perimeter of this face. The largest face is the one with dimensions 8 cm x 4 cm.

The perimeter (P) of the rectangle is calculated as:
\[ P = 2(L + B) \]
Substituting the values:
\[ P = 2(8 \, \text{cm} + 4 \, \text{cm}) = 2(12 \, \text{cm}) = 24 \, \text{cm} \]

### Step 3: Use the formula for surface tension
Surface tension (T) is defined as the force (F) per unit length (L):
\[ T = \frac{F}{L} \]
Where:
- T = surface tension of water = \( 7.2 \times 10^{-4} \, \text{N/cm} \)
- L = perimeter of the frame in contact with water = 24 cm

### Step 4: Rearrange the formula to find the force
Rearranging the formula to find the force gives us:
\[ F = T \times L \]

### Step 5: Substitute the values into the equation
Now, substituting the values we have:
\[ F = (7.2 \times 10^{-4} \, \text{N/cm}) \times (24 \, \text{cm}) \]

### Step 6: Calculate the force
Calculating the force:
\[ F = 7.2 \times 24 \times 10^{-4} \]
\[ F = 172.8 \times 10^{-4} \, \text{N} \]
\[ F = 1.728 \times 10^{-2} \, \text{N} \]

### Final Answer
The downward force acting on the frame due to the surface tension of water is:
\[ F = 1.728 \times 10^{-2} \, \text{N} \]

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