Explanation :
We know that the centripetal force always acting towards the center of a circle. Mathematically, it is given as :
[tex]a_c=\dfrac{v^2}{r}[/tex].........(1)
v is the velocity of an object moving in circular motion, [tex]v=\dfrac{2\pi r}{T}[/tex]
r is the radius of the circle
T is the time taken by an object.
Put he value of v is equation (1)
[tex]a_c=\dfrac{1}{r}(\dfrac{2\pi r}{T})^2[/tex]
[tex]a_c=\dfrac{4\pi^2 r}{T^2}[/tex]
