Question

Sandy is whirling a ball attached to a string in a horizontal circle over his head. If Sandy doubles the speed of the ball, what happens to the tension in the string?
A) It doubles.
B) It quadruples.
C) It is cut in half.
D) It remains constant.

Answer 1

The tension in the string B) It quadruples.

Explanation:

The ball is in uniform circular motion in a horizontal circle, so the tension in the string is providing the centripetal force that keeps the ball in circular motion. So we can write:

$T= m\frac{v^2}{r}$

where:

T is the tension in the string

m is the mass of the ball

v is the speed of the ball

r is the radius of the circle (the lenght of the string)

In this problem, we are told that the speed of the ball is doubled, so

v' = 2v

Substituting into the previous equation, we find the new tension in the string:

$T' = m \frac{(2v)^2}{r}=4(m\frac{v^2}{r})=4T$

Therefore, the tension in the string will quadruple.

Learn more about circular motion:

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