A mosquito with 8 legs stands on water surface and each leg makes depression of radius 'a'. If the surface tension and angle of contact are 'T' and zero respectively, then the weight of mosquito is:

Options

A. 8 Ta
B. `16 pi Ta`
C. `(Ta)/8`
D. `(Ta)/(16pi)`

Answer

To solve the problem, we need to determine the weight of the mosquito based on the given parameters: the number of legs, the radius of the depression made by each leg, the surface tension, and the angle of contact.

### Step-by-Step Solution:

1. **Identify the Parameters**:
- Number of legs (n) = 8
- Radius of depression (r) = a
- Surface tension (T) = T
- Angle of contact = 0 (which implies that the surface tension acts vertically upward)

2. **Understand the Concept of Surface Tension**:
- Surface tension (T) creates a force that acts along the surface of the liquid. When a leg of the mosquito depresses the water surface, it creates a circular depression with radius 'a'.
- The force due to surface tension acting on the circular depression is given by the formula:
\[ \text{Force} = \text{Surface Tension} \times \text{Perimeter of the depression} \]
- The perimeter of a circle (depression) is given by \(2\pi r\).

3. **Calculate the Force for One Leg**:
- For one leg, the force due to surface tension is:
\[ F_{\text{one leg}} = T \times (2\pi a) \]

4. **Calculate the Total Force for All Legs**:
- Since the mosquito has 8 legs, the total upward force (which balances the weight of the mosquito) is:
\[ F_{\text{total}} = 8 \times F_{\text{one leg}} = 8 \times (T \times 2\pi a) \]
- Simplifying this gives:
\[ F_{\text{total}} = 16\pi a T \]

5. **Weight of the Mosquito**:
- The weight of the mosquito (W) is equal to the total force exerted by the surface tension, hence:
\[ W = 16\pi a T \]

### Final Answer:
The weight of the mosquito is \( W = 16\pi a T \).