Force necessary to pull a circular plate of 5 cm radius from water surface for which surface tension is 75 dynes/cm, is

Options

A. (a)30 dynes
B. (b)60 dynes
C. (c)750 dynes
D. (d)`750pi` dynes

Answer

To find the force necessary to pull a circular plate of 5 cm radius from the water surface, given that the surface tension is 75 dynes/cm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Radius of the circular plate (r) = 5 cm
- Surface tension (T) = 75 dynes/cm

2. **Calculate the Circumference of the Circular Plate:**
- The total length (L) around which the surface tension acts is the circumference of the circular plate.
- The formula for the circumference (C) of a circle is:
\[ C = 2 \pi r \]
- Substituting the value of r:
\[ C = 2 \pi (5 \text{ cm}) = 10 \pi \text{ cm} \]

3. **Calculate the Force Required to Pull the Plate:**
- The force (F) required to pull the plate is given by the product of the surface tension (T) and the length (L) around which it acts:
\[ F = T \times L \]
- Substituting the values:
\[ F = 75 \text{ dynes/cm} \times 10 \pi \text{ cm} \]
- This simplifies to:
\[ F = 750 \pi \text{ dynes} \]

4. **Final Calculation:**
- The numerical value of \( F \) can be approximated using \( \pi \approx 3.14 \):
\[ F \approx 750 \times 3.14 \approx 2355 \text{ dynes} \]

5. **Conclusion:**
- The force necessary to pull the circular plate from the water surface is approximately \( 750 \pi \) dynes.