Final answer:
The acceleration of an object traveling at double the speed and in a circle with double the radius is four times the original acceleration a. The formula for centripetal acceleration is used to determine that the correct answer is c) 4a.
Step-by-step explanation:
The student's question deals with centripetal acceleration in circular motion. Centripetal acceleration (ac) is given by the formula ac = v2/r, where v is the speed of the object and r is the radius of the circle. In this case, the acceleration of the object moving at speed 2V in a circle of radius R is a.
If both the speed and radius are doubled, the new speed is 4V (since 2V doubled is 4V), and the new radius is 2R (since R doubled is 2R). Therefore, the new centripetal acceleration using the formula would be ac' = (4V)2/(2R) = 16V2/(2R) = 8V2/R = 8a, which implies the new acceleration is 4 times the original acceleration a. Hence, the answer to the student's multiple-choice question is c) 4a.