Question

A 1000-g ball is tied to a string 60cm long and is whirled in a vertical circle at 1 revolution per second. if the tension at the highest point is zero what is the speed of the body at the highest point?

Answer 1

The second Newton's law for the highest point:

$$ma = mg+T$$

where $a = \dfrac{v^2}{r}$ is the centripetal acceleration ($v$ is the speed of the ball, $r = 60cm = 0.6m$ is the radius of the circle), and $T = 0$ is the tension of the string. $m = 1000g = 1kg$ and $g = 9.81m/s^2$ is the gravitational acceleration. Thus, expressing $v$ obtain:

$$m\dfrac{v^2}{r} = mg\\ v = \sqrt{rg}\\ v = \sqrt{0.6\cdot 9.81} \approx 2.4m/s$$

Answer. 2.4m/s.