To address your question about the forces acting on a car moving in a circular path, let’s break down the concepts of centripetal and centrifugal forces, and clarify why we consider them in the way described in the problem from H.C. Verma.

Understanding Forces in Circular Motion

When an object moves in a circular path, it experiences a change in direction, which requires a net force acting towards the center of the circle. This inward force is known as the centripetal force. In the case of a car on a curved road, this force is typically provided by friction between the tires and the road surface.

Centripetal Force Explained

The centripetal force can be calculated using the formula:

• F_c = mv²/r

Here, m is the mass of the car, v is its velocity, and r is the radius of the circular path. This force acts towards the center of the circle, allowing the car to maintain its curved trajectory.

The Role of Gravity

Gravity also plays a crucial role in this scenario. The weight of the car, given by mg (where g is the acceleration due to gravity), acts downwards. When analyzing forces in a vertical circular motion, we need to consider both the gravitational force and the centripetal force together.

Why Centrifugal Force Comes Into Play

Centrifugal force is often described as a "fictitious" force that appears when we analyze motion from a rotating reference frame. In this context, it seems to act outward, away from the center of the circle. While it is not a real force acting on the car, it helps us understand the perspective of an observer in the rotating frame.

Balancing Forces

In the scenario you mentioned, when considering the forces acting on the car, we can set up the following equation based on the forces acting in the vertical direction:

• Net Force = Centripetal Force - Weight
• mv²/r = mg - R

Here, R is the normal reaction force from the road. Rearranging gives us:

• R = mg - mv²/r

This equation shows that the normal force is affected by both the weight of the car and the required centripetal force. If we were to consider centrifugal force, we would be looking at it from the perspective of the car's frame, where the outward force seems to push the car away from the center. However, in a non-accelerating frame (like the ground), we focus on the actual forces acting on the car.

Conclusion on Force Consideration

In summary, while centripetal force is essential for keeping the car in circular motion, centrifugal force is a helpful concept for understanding the effects of inertia from a rotating frame. In problems like the one from H.C. Verma, we focus on the real forces acting on the car, which include gravity and the normal force, rather than introducing fictitious forces that can complicate the analysis. This approach helps us accurately determine the conditions for safe circular motion.