If a body moves with a constant speed in a circle

Options

A. no work is done on it
B. no force acts on it
C. no acceleration is produced in it
D. its velocity remains constant

Answer

### Step-by-Step Solution:

1. **Understanding Circular Motion**:
- A body moving in a circle at a constant speed is undergoing circular motion. While the speed (magnitude of velocity) remains constant, the direction of the velocity vector changes continuously.

2. **Acceleration in Circular Motion**:
- Even though the speed is constant, the body experiences centripetal acceleration directed towards the center of the circle. This acceleration is given by the formula:
\[ a_c = \frac{v^2}{r} \]
where \( v \) is the constant speed and \( r \) is the radius of the circle.

3. **Velocity vs Speed**:
- It's important to differentiate between speed and velocity. Speed is a scalar quantity (only magnitude), while velocity is a vector (magnitude and direction). In circular motion, although the speed remains constant, the direction of the velocity changes, meaning the velocity is not constant.

4. **Forces Acting on the Body**:
- For an object to move in a circle, there must be a net force acting towards the center of the circle, known as centripetal force. This force is responsible for changing the direction of the velocity vector. The centripetal force can be expressed as:
\[ F_c = m \cdot a_c = m \cdot \frac{v^2}{r} \]
where \( m \) is the mass of the body.

5. **Work Done on the Body**:
- Work done is defined as the product of the force and the displacement in the direction of the force. In circular motion, the centripetal force acts perpendicular to the displacement of the body (which is tangential to the circle). Since the angle between the force and displacement is 90 degrees, the work done is:
\[ W = F \cdot d \cdot \cos(\theta) = F \cdot d \cdot \cos(90^\circ) = 0 \]
Thus, no work is done on the body.

### Conclusion:
- In summary, while a body moves in a circle at constant speed:
- It experiences centripetal acceleration.
- Its velocity is not constant due to changing direction.
- There is a centripetal force acting on it.
- No work is done on the body since the force is perpendicular to the displacement.