A stone of mass m tied to the end of a string revolves in a vertical circle of radius R. The net forces at the lowest and highest points of the circle directed vertically downwards are: [Choose the correct alternative] Lowest point Highest point
`T_(1)` and `V_(1)` denote the tension and speed at the lowest point `T_(2)` and `V_(2)` denote the corresponding values at the highest points.

Explanation

To solve the problem of a stone of mass \( m \) tied to a string revolving in a vertical circle of radius \( R \), we need to analyze the forces acting on the stone at both the lowest and highest points of the circle.

### Step-by-Step Solution:

1. **Identify Forces at the Lowest Point:**
At the lowest point of the circle, the forces acting on the stone are:
- The gravitational force acting downwards: \( mg \)
- The tension in the string acting upwards: \( T_1 \)

The net force \( F_{\text{net, low}} \) at the lowest point can be expressed as:
\[ F_{\text{net, low}} = T_1 - mg \]

2. **Identify Forces at the Highest Point:**
At the highest point of the circle, the forces acting on the stone are:
- The gravitational force acting downwards: \( mg \)
- The tension in the string acting downwards: \( T_2 \)

The net force \( F_{\text{net, high}} \) at the highest point can be expressed as:
\[ F_{\text{net, high}} = mg + T_2 \]

3. **Understand the Role of Centripetal Force:**
For the stone to maintain circular motion, the net force at both points must provide the necessary centripetal force required to keep the stone moving in a circle. The centripetal force \( F_c \) is given by:
\[ F_c = \frac{mv^2}{R} \]
where \( v \) is the speed of the stone at that point.

4. **Set Up Equations for Circular Motion:**
- At the lowest point:
\[ T_1 - mg = \frac{mv_1^2}{R} \quad \text{(1)} \]
- At the highest point:
\[ mg + T_2 = \frac{mv_2^2}{R} \quad \text{(2)} \]

5. **Summarize the Net Forces:**
From the above equations, we can summarize the net forces:
- At the lowest point: \( T_1 = mg + \frac{mv_1^2}{R} \)
- At the highest point: \( T_2 = \frac{mv_2^2}{R} - mg \)

### Conclusion:
The net forces acting on the stone at the lowest and highest points are:
- **Lowest Point:** \( T_1 - mg \) (upward)
- **Highest Point:** \( mg + T_2 \) (downward)