Question

At any instant, the magnitude of the centripetal force on a particle of mass \( m \) performing circular motion is given by

• A. \( \frac{m^2 \omega^2}{v} \)
• B. \( \frac{m \omega^2}{v} \)
• C. \( \frac{mv^2}{\omega} \)
• D. \( m \omega v \)

Hint:

The centripetal force is always directed towards the center of the circular path and depends on the mass, velocity, and radius of the path.

Answer 1

The Correct Option is D

Step 1: Understanding centripetal force.
The centripetal force \( F_c \) on a particle moving in a circle of radius \( r \) with velocity \( v \) is given by: \[ F_c = \frac{mv^2}{r} \] Since \( v = r\omega \), where \( \omega \) is the angular velocity, the expression for centripetal force becomes: \[ F_c = m \omega v \] Step 2: Conclusion.
Thus, the magnitude of the centripetal force is \( m \omega v \), corresponding to option (D).