A body is tided with a string and is given a circular motion with velocity v in radius r. The magnitude of the acceleration is

Options

A. `v/r`
B. `v^(2)/r`
C. `v/v^(2)`
D. `v^(2)/r^(2)`

Explanation

To find the magnitude of the acceleration of a body undergoing circular motion, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Circular Motion**:
- A body tied to a string and rotated in a circular path is undergoing uniform circular motion. In this type of motion, the speed of the body remains constant, but the direction of the velocity changes continuously.

2. **Identifying Forces**:
- The only force acting on the body that keeps it in circular motion is the tension in the string. This tension provides the necessary centripetal force required for circular motion.

3. **Centripetal Force**:
- The formula for centripetal force \( F_c \) is given by:
\[ F_c = \frac{mv^2}{r} \]
where \( m \) is the mass of the body, \( v \) is the velocity, and \( r \) is the radius of the circular path.

4. **Relating Force to Acceleration**:
- According to Newton's second law, the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the centripetal force is the net force acting on the body:
\[ F_c = m \cdot a_c \]
where \( a_c \) is the centripetal acceleration.

5. **Setting the Equations Equal**:
- Since both expressions represent the centripetal force, we can set them equal to each other:
\[ m \cdot a_c = \frac{mv^2}{r} \]

6. **Solving for Acceleration**:
- We can cancel the mass \( m \) from both sides (assuming \( m \neq 0 \)):
\[ a_c = \frac{v^2}{r} \]

7. **Conclusion**:
- The magnitude of the acceleration (centripetal acceleration) of the body in circular motion is given by:
\[ a_c = \frac{v^2}{r} \]

### Final Answer:
The magnitude of the acceleration is \( \frac{v^2}{r} \).

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