Answer:
The tension increases by a factor of 8
Explanation:
We know that the tension, T in the string equals the centripetal force on the ball. So
T = mrω² = mr(2πf)² = 4mrπ²f² where m = mass of ball, r = radius of circle and f = frequency of rotation
If the radius and frequency are doubled, then r = 2r and f = 2f. So, the new tension is T' = 4mr'π²f'² = 4m(2r)π²(2f)² = 4 × 2 × 4mrπ²f² = 8T
Since T' = 8T,
So T'/T = 8.
So the tension increases by a factor of 8
