Answer:
If both the radius and frequency are doubled, then the tension is increased 8 times. 
Explanation:
The radial acceleration ( ), measured in meters per square second, experimented by the moving end of the string is determined by the following kinematic formula:
), measured in meters per square second, experimented by the moving end of the string is determined by the following kinematic formula:
 (1)
 (1)
Where:
 - Frequency, measured in hertz.
 - Frequency, measured in hertz.
 - Radius of rotation, measured in meters.
 - Radius of rotation, measured in meters.
From Second Newton's Law, the centripetal acceleration is due to the existence of tension ( ), measured in newtons, through the string, then we derive the following model:
), measured in newtons, through the string, then we derive the following model:
 (2)
 (2)
Where  is the mass of the object, measured in kilograms.
 is the mass of the object, measured in kilograms. 
By applying (1) in (2), we have the following formula:
 (3)
 (3)
From where we conclude that tension is directly proportional to the radius and the square of frequency. Then, if radius and frequency are doubled, then the ratio between tensions is:
 (4)
 (4)


If both the radius and frequency are doubled, then the tension is increased 8 times.