Question

A particle of mass M moves with constant speed along a circular path of radius r under the action of a force F. Find its speed.
A. \[\sqrt {\dfrac{{Fr}}{m}} \]
B. \[\sqrt {\dfrac{F}{r}} \]
C. \[\sqrt {Fmr} \]
D. \[\sqrt {\dfrac{F}{{mr}}} \]

Answer 1

Hint: Before we start addressing the problem, we need to know about the centripetal force. The force which acts on the object when it is moving in any of the circular paths is known as the centripetal force. This force acts toward the center hence the name centripetal force.

Formula Used:
The centripetal force is,
\[F = \dfrac{{m{v^2}}}{r}\]
Where, r is radius, v is velocity and m is mass.

Complete step by step solution:
Here, the particle is moving in a circular path, which means it is under the circular motion. Anybody which is performing the circular motion must possess a centripetal force that is always directed towards the center and it is not a fundamental force, some other force must behave like a centripetal force.

In this case, they have mentioned the body moves under constant force F in a circular path, which means the force that acts on the body is centripetal force.
The magnitude of centripetal force is,
\[F = \dfrac{{m{v^2}}}{r}\]

Here, we need to find the speed v,
Therefore,
\[{v^2} = \dfrac{{Fr}}{m}\]
\[v = \sqrt {\dfrac{{Fr}}{m}} \]
Therefore, the speed of a particle is \[\sqrt {\dfrac{{Fr}}{m}} \].

Hence, Option A is the correct answer.

Note:In this problem it is important to remember that in order to find the speed of any object which is moving in a circular motion the necessary force that comes into existence is centripetal force. Using the formula of centripetal force we are going to find the speed of any object or particle.