Final answer:
The centripetal acceleration increases by a factor of 36 when the velocity is increased by a factor of 6, considering that centripetal acceleration is directly proportional to the square of the velocity.
Step-by-step explanation:
The question asks by what factor the centripetal acceleration changes if the velocity changes by a factor of 6. Centripetal acceleration is given by the formula ac = v²/r, where v is the velocity of the object and r is the radius of the circular path. If the velocity v is increased by a factor of 6, the new velocity is '6v'. Therefore, the new centripetal acceleration will be '(6v)²/r' which is '36v²/r', indicating that the centripetal acceleration has increased by a factor of 36. Hence, the answer to the question is C) 36.