Question

The magnitude of the centripetal force acting on a body of mass m executing uniform motion in a circle of radius r with speed v is ?
A. $mvr$
B. $\dfrac{m{{v}^{2}}}{r} \\ $
C. $\,\dfrac{v}{{{r}^{2}}m} \\ $
D. $\dfrac{v}{rm}$

Answer 1

Hint: To solve this problem, we just need to know the concepts of centripetal force. We must also know the concepts of uniform circular motion. If we know the basics then we can attend these questions easily.

Formula used:
The expression of centripetal acceleration is,
$a=\dfrac{{{v}^{2}}}{r}$
Where, $v$ is the velocity of a body and $r$ is the radius of curvature.

Complete step by step solution:
Newton’s law of motions is not valid in all frames of references. Centrifugal force is the outward force acting on a body when it is rotated. In an inertial frame no outward acceleration is observed since the system is not rotating. Centripetal force is the inward force acting on the body moving in a circular motion.

If a particle is moving in a circle in an inertial frame, a resultant nonzero force must act on the particle. It is because particles moving in a circular motion are accelerated and acceleration produced in an inertial frame of reference is because of the resultant force acting on it. If the particle is moving with a constant speed in a circle, then the acceleration experienced will be towards the centre.

Let r be the radius of the circle, m be the mass of the particle, v be the velocity of the particle and a be the acceleration and F be the resultant centripetal force acting on the particle. Then magnitude of acceleration,
$a=\dfrac{{{v}^{2}}}{r}$
We also know that acceleration,
$a=\dfrac{F}{m}$
On equation we get magnitude of centripetal force as:
$F=\dfrac{m{{v}^{2}}}{r}$
This resultant force is acting towards the centre.

Therefore, the correct answer is option B.

Notes: Often people get confused by centripetal force and centrifugal force. Centripetal force is required for the circular motion and centrifugal force is that makes something flee from the centre. Actually, both have the same magnitude but with opposite signs. Centripetal force is real and centrifugal force is pseudo force.