How can I solve this please help?

Question

A light, rigid rod is 65.2 cm long. Its top end is pivoted on a frictionless horizontal axle. The rod hangs straight down at rest with a small, massive ball attached to its bottom end. You strike the ball, suddenly giving it a horizontal velocity so that it swings around in a full circle. What minimum speed at the bottom is required to make the ball go over the top of the circle?

 _____ m/s

Answer 1

Let

h = 65.2cm be the length of the rod

m be the mass of the ball

v be the minimum speed to make the ball go over the top

g = 9.8 m/s² be gravitational acceleration

We use conservation of energy.

The kinetic energy imparted to the ball at the bottom (mv²/2)

needs to convert to the potential energy of the ball at the top (2hmg)

mv²/2 = 2hmg

v = sqrt(4hg) = 2sqrt(hg)

= 2sqrt(65.2 cm . 9.8 m/s²)

= 2sqrt(65.2 . 0.01 m . 9.8 m/s²)

= 5 m/s