Dynamics of Uniform Circular Motion - Centripetal Force

A particle of mass m is observed from an inertial frame of reference and is found to move in a circle of radius r with a uniform speed v. The centrifugal force on it is 

A racing car completes 5 rounds of a circular track in 2 minutes. Find the radius of the track
if the car has uniform centripetal acceleration of Π² m/s².

Consider the circular motion of the Earth around the sun. Which of the following statements is more appropriate?

(a) Gravitational attraction of the sun on the earth is equal to the centripetal force.
(b) The gravitational attraction of the sun on the earth is the centripetal force.

A particle of mass m, just completes the vertical circular motion. Derive the expression for the difference in tensions at the highest and the lowest points.

Explain the concept of centripetal force.

A particle of mass m rotates with a uniform angular speed ω. It is viewed from a frame rotating about the Z-axis with a uniform angular speed ω₀. The centrifugal force on the particle is 

A heavy mass m is hanging from a string in equilibrium without breaking it. When this same mass is set into oscillation, the string breaks. Explain.