Question

A ball swings in a horizontal circle. If the radius and the frequency are both doubled, by what factor does the tension in the string increase?

Answer 1

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