The force required to lift a circular flat plate of radius 5 cm on the surface of water is: (Surface tension of water is 75 dyne/cm):-

Options

A. 30 dyne
B. 60 dyne
C. 750 dyne
D. 750 `pi` dyne

Answer

To solve the problem of finding the force required to lift a circular flat plate of radius 5 cm on the surface of water, we can follow these steps:

### Step 1: Understand the concept of surface tension
Surface tension is the force per unit length acting at the surface of a liquid. It acts along the surface and tends to minimize the surface area. For a circular plate, the force required to lift it from the water is directly related to the surface tension and the circumference of the plate.

### Step 2: Calculate the circumference of the circular plate
The circumference \( C \) of a circle is given by the formula:
\[ C = 2\pi r \]
where \( r \) is the radius of the circle. For our plate, the radius \( r \) is 5 cm.
\[ C = 2\pi \times 5 \, \text{cm} = 10\pi \, \text{cm} \]

### Step 3: Use the surface tension to find the force
The force \( F \) required to lift the plate can be calculated using the formula:
\[ F = \text{Surface Tension} \times \text{Length} \]
where the length in this case is the circumference of the plate. The surface tension of water is given as 75 dyne/cm.

Substituting the values:
\[ F = 75 \, \text{dyne/cm} \times 10\pi \, \text{cm} \]

### Step 4: Perform the multiplication
Now, calculate the force:
\[ F = 75 \times 10\pi \, \text{dyne} = 750\pi \, \text{dyne} \]

### Conclusion
The force required to lift the circular flat plate of radius 5 cm on the surface of water is:
\[ F = 750\pi \, \text{dyne} \]

### Final Answer
Thus, the answer is \( 750\pi \, \text{dyne} \).

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