A body is revoving with a constant speed along a circle. If its direction of motion is reversed but the speed remains the same, then which of the following statement is true

Options

A. the cetripetal force will not surffer any change in magnitude
B. the centripetal force will have its direction reversed
C. the centripetal force will not suffer any change in direction
D. the centripetal force would be doubled

Explanation

To solve the problem, we need to analyze the situation where a body is revolving in a circle with a constant speed and then its direction of motion is reversed while maintaining the same speed.

### Step-by-Step Solution:

1. **Understanding Circular Motion**:
- A body moving in a circle experiences centripetal force directed towards the center of the circle. The magnitude of this force is given by the formula:
\[ F_c = \frac{mv^2}{r} \]
where \( m \) is the mass of the body, \( v \) is the speed, and \( r \) is the radius of the circle.

**Hint**: Remember that centripetal force is always directed towards the center of the circular path.

2. **Initial Direction of Motion**:
- Assume the body is moving in a clockwise direction with speed \( v \). The centripetal force is directed towards the center of the circle.

**Hint**: Visualize the circular path and the direction of motion to understand how forces act.

3. **Reversing the Direction**:
- When the direction of motion is reversed, the body will now move in a counterclockwise direction, but the speed \( v \) remains the same.

**Hint**: Consider how reversing the direction affects the motion but not the speed.

4. **Centripetal Force After Reversal**:
- Regardless of the direction of motion (clockwise or counterclockwise), the centripetal force will still act towards the center of the circle. The magnitude of the centripetal force remains:
\[ F_c = \frac{mv^2}{r} \]
This means that the magnitude of the centripetal force does not change.

**Hint**: Focus on the fact that centripetal force always points towards the center, irrespective of the direction of motion.

5. **Evaluating the Statements**:
- From the analysis:
- The centripetal force does not change in magnitude.
- The direction of the centripetal force remains directed towards the center, regardless of the direction of motion.
- The centripetal force is not doubled; it remains the same.

**Hint**: Compare the statements provided in the question with your findings.

### Conclusion:
Based on the analysis, the correct statements are:
1. The centripetal force will not suffer any change in magnitude.
2. The centripetal force will have its direction reversed. (This statement is incorrect; it remains directed towards the center.)
3. The centripetal force would be double. (This statement is incorrect; it remains the same.)

Thus, the only true statement is that the centripetal force does not change in magnitude.

### Final Answer:
- The centripetal force will not suffer any change in magnitude.