A particle of mass 5kg is moving in circular motion with a time period of 2 seconds. The radius of the circle is 10m. What is the centripetal force on the particle

The angular velocity is equal to 2 times pi divided by the time period. So we have an angular velocity of pi radians per second. The centripetal force is given by mass times the radius times the angular velocity squared so, 5x10xpi=50pi which is approximately 157.08N.