Explain the centripetal force.

Hint: The centripetal force is the force which acts perpendicular to the direction of velocity and it can be shown mathematically as, ${{F}_{c}}=\dfrac{m{{v}^{2}}}{r}$. Using this principle and formula we will further explain the centripetal force acting on an object.

Formula used: ${{F}_{c}}=\dfrac{m{{v}^{2}}}{r}$

Complete step by step answer:
The centripetal force acts on the object when the object is performing a circular motion. This force is also responsible in making the body follow the circular path. The direction of the force is always orthogonal to the motion of the body and acting towards the centre of the curvature. This can be seen in the figure,

Now, this force can be seen mathematically as,
${{F}_{c}}=\dfrac{m{{v}^{2}}}{r}$
Where m is the mass of an object, v is velocity, r is radius of curvature and ${{F}_{c}}$ is the centripetal force.
Now, in Newtonian physics, the centripetal force is responsible for the motion of astronomical objects. Even in the case of a satellite when it is in orbit around any planet the gravity acting on that satellite is due to centripetal force. Though the orbits are eccentric the centripetal force acts on the focus and not on the centre of curvature.
Now, in the case of an object that is swinging around on the end of a rope in a horizontal plane, the centripetal force on the object is supplied by the tension of the rope. The same thing happens when a death rider in a circus rides on the circular walls by balancing himself according to the centripetal force acting on him and his bike.

Note: Students should not get confused with the centripetal force acting on the body and the centrifugal force acting on the body. As both forces are almost same but the main difference between them is that the centripetal force acts towards the centre of curvature of circular path while the centrifugal force acts in the opposite direction to the centripetal force. Thus, students should know this difference and then solve the problem.