[quote]
Now as the rotating body is subjected to a force  directed towards centre, it should move towards centre according to Newton's 2nd law. [/quote]

Newton's Law only indicated that acceleration is in the same direction of the net force. [b]F[/b]=m [b]a[/b]
Acceleration is the rate of velocity change. So it is in the direction of difference between two velocity.

By the way, circular motion or means that it is moving in circle.