A 1 kg stone at the end of 1 m long string is whirled in a vertical circle at constant speed of 4 m/sec. The tension in the string is 6 N when the stone is at `(g =10m//sec^(2))`

Options

A. top of the cirlce
B. bottom of the circle
C. half way down
D. none of the above

Explanation

To solve the problem step by step, we will analyze the forces acting on the stone when it is in a vertical circular motion. We will determine the position of the stone based on the given tension and speed.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Mass of the stone, \( m = 1 \, \text{kg} \)
- Length of the string (radius of the circle), \( r = 1 \, \text{m} \)
- Speed of the stone, \( v = 4 \, \text{m/s} \)
- Tension in the string, \( T = 6 \, \text{N} \)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \)

2. **Determine the Centripetal Force:**
The centripetal force required to keep the stone moving in a circle is given by:
\[ F_c = \frac{mv^2}{r} \]
Substituting the values:
\[ F_c = \frac{1 \times (4)^2}{1} = \frac{16}{1} = 16 \, \text{N} \]

3. **Analyze Forces at Different Positions:**
- At the **top of the circle**, the tension and gravitational force both act downwards. The equation for the forces is:
\[ T + mg = F_c \]
Substituting the known values:
\[ 6 + (1 \times 10) = 16 \]
This simplifies to:
\[ 16 = 16 \quad \text{(True)} \]
- At the **bottom of the circle**, the tension acts upwards while the gravitational force acts downwards. The equation for the forces is:
\[ T - mg = F_c \]
Substituting the known values:
\[ T - 10 = 16 \]
Rearranging gives:
\[ T = 16 + 10 = 26 \, \text{N} \]
This is inconsistent with the given tension of 6 N.

4. **Conclusion:**
Since the only position where the calculated forces match the given tension of 6 N is at the **top of the circle**, we conclude that the stone is at the top of the circle when the tension in the string is 6 N.

### Final Answer:
The stone is at the **top of the circle**.