A particle of mass m is observed from an inertial frame of reference and is found to move in a circle of radius r with a uniform speed v. The centrifugal force on it is

Options

A. `(mv^2)/r` towards the centre
B. `(mv^2)/r` away from the centre
C. `(mv^2)/r` along the tangent through the particle
D. zero

Answer

To solve the problem, we need to analyze the situation of a particle moving in a circular path from an inertial frame of reference. Here are the steps to arrive at the solution:

### Step-by-Step Solution:

1. **Understanding Circular Motion**:
The particle of mass \( m \) is moving in a circle of radius \( r \) with a uniform speed \( v \). In circular motion, the particle experiences a centripetal force directed towards the center of the circle, which keeps it in its circular path.

2. **Centripetal Force**:
The centripetal force \( F_c \) required to keep the particle moving in a circle is given by the formula:
\[ F_c = \frac{mv^2}{r} \]
where \( m \) is the mass of the particle, \( v \) is the speed, and \( r \) is the radius of the circle.

3. **Centrifugal Force**:
The centrifugal force is considered a pseudo force that appears when analyzing motion from a rotating frame of reference. It acts outward, away from the center of the circular path. However, it is important to note that this force is not present in an inertial frame of reference.

4. **Inertial Frame of Reference**:
Since the observer is in an inertial frame (non-accelerating), they do not experience the effects of centrifugal force. In this frame, the only force acting on the particle is the centripetal force directed towards the center of the circle.

5. **Conclusion**:
Therefore, from the perspective of an observer in an inertial frame, the centrifugal force acting on the particle is zero.

Thus, the answer to the question is:
\[ \text{Centrifugal Force} = 0 \]

### Final Answer:
The centrifugal force on the particle is \( 0 \).

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