One end of a string of length $l$ is connected to a particle of mass $m$ and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed $v$ the net force on the particle ( directed towards the centre ) is :

When a particle connected to a string revolves in a circular path around a center, the centripetal force is provided by the tension produced in the string. Hence, in the given case, the net force on the particle is the tension $T$, i.e., 
$F=T=\frac{m{v}^2}{l}$
Where $F$ is the net force acting on the particle.