Answers below in the second screenshot **Problem:**A car goes around a curve of a radius \( r \) at a constant speed \( v \). Then it goes around the same curve at half of the original speed. Which of the following correctly identifies the change in force and the reason for it to occur?**Options:**1) The centripetal force increases by a factor of 2 because velocity and force are directly proportional when an object is traveling along a circular path.2) The centripetal force decreases by a factor of 4 because velocity and force have a proportional, but squared, relationship when an object is traveling along a circular path.3) The centripetal force increases by a factor of 1/2 because velocity and force have a proportional, but squared, relationship when an object is traveling along a circular path.4) The centripetal force decreases by a factor of 1/4 because velocity and force have a proportional, but squared, relationship when an object is traveling along a circular path.

The centripetal force acting on an object moving in the circular path is given by the below formula as F =mv2/r m is the mass of the object v is the speed of object r is the radius of circular If the object moves in same curve at half of the original speed, v' = v/2 New centripetal force is then given by F' = m v'2/r Put v' = v/2 So F' = 1/4 × m v2/r F'= F/4 , the new centripetal force becomes one fourth of the original forceOption 4 correct answers 4) The centripetal force decrease by a factor of 1/4 because velocity and force have a proportional but squared relationship when an object is traveling along a circular path.