Question

The formula used to calculate centrifugal force is
A. $$F=ma$$; a is the acceleration of the particle, which is a constant
B. $$F=m{\displaystyle \frac{dv}{dt}}$$; $${\displaystyle \frac{dv}{dt}}$$ is the rate of change velocity of the particle moving in a straight line
C. $$F=m{v}^2/R$$
D. Centrifugal force cannot be calculated

Answer 1

Hint: The centrifugal force is the force that has the same magnitude as that of centripetal force but it has the opposite direction. In the uniform circular motion, the velocity of the particle changes the direction at each point. The magnitude of the velocity does not change in the uniform circular motion.

Complete step by step answer:
We are familiar with the two forces in the circular motion: centripetal force and centrifugal force. The centripetal force is the force that acts on the particle in the circular motion along the radius towards the centre of the circular motion. The centrifugal force is the force which has the same magnitude as that of centripetal force but it has the opposite direction.

We know that the acceleration of the particle in the circular motion is given as,
$$a={\displaystyle \frac{v^2}{r}}$$, where, v is the velocity and r is the radius of the circular motion.
In the circular motion, the acceleration of the particle is not constant since the velocity of the particle always changes the direction at each point.

The force acting on the particle of mass m which has acceleration $${\displaystyle \frac{v^2}{r}}$$ is,
$$F={\displaystyle \frac{m{v}^2}{r}}$$
The above expression is known as centripetal force acting on the particle revolving in the uniform circular motion. Since the centrifugal force has the same magnitude as that of the centripetal force, the formula for the centrifugal force will be,
$$\therefore F={\displaystyle \frac{m{v}^2}{r}}$$

So, the correct answer is option C.

Note: The acceleration of the particle in the circular motion is not constant. Also, the magnitude of the velocity in the uniform circular motion does not change and only the direction of the velocity changes. The direction of the centrifugal force is always in the outward direction of the motion.