Radial and Tangential Accelerations in Circular Motion

Circular motion is the motion of an object along a circular path. When a body moves along a circular path with variable speed, it experiences both radial and tangential accelerations.

Radial Acceleration:
- Radial acceleration is the acceleration that acts towards the center of the circle. It is responsible for changing the direction of the velocity vector.
- The magnitude of radial acceleration can be calculated using the equation ar = v^2 / r, where v is the magnitude of the velocity and r is the radius of the circular path.
- Radial acceleration is always directed towards the center of the circle and its value depends on the magnitude of the velocity and the radius of the circular path.
- In circular motion with variable speed, the magnitude of the velocity changes, so the radial acceleration also changes.

Tangential Acceleration:
- Tangential acceleration is the acceleration that acts tangent to the circular path. It is responsible for changing the magnitude of the velocity vector.
- The magnitude of tangential acceleration can be calculated using the equation at = dv / dt, where dv is the change in velocity and dt is the change in time.
- Tangential acceleration is always directed tangent to the circular path and its value depends on the rate of change of velocity.
- In circular motion with variable speed, the magnitude of the velocity changes, so the tangential acceleration also changes.

Explanation of the Correct Answer:
- In the given question, the body is moving along a circular path with variable speed. Since the speed is variable, it means that the magnitude of the velocity is changing.
- As explained earlier, when the magnitude of the velocity changes, both radial and tangential accelerations are present.
- Therefore, the correct answer is option 'D' which states that the body experiences both tangential and radial accelerations in this scenario.

In conclusion, when a body moves along a circular path with variable speed, it experiences both radial and tangential accelerations. The radial acceleration is responsible for changing the direction of the velocity vector, while the tangential acceleration is responsible for changing the magnitude of the velocity vector.