A 1.5 kg tether ball is hit so that it circles the pole with an angular speed of 4m/s

Well, you didn't ask a question, and 4 m/s is not an angular speed.

So all I can offer is a couple of observations:

1). The tension in the rope is

M V² / R = (1.5 kg) x (4 m/s) ² / R

= (24 kg-m²/s²) / (distance of the ball from the pole).

2). Tetherball was the only thing I played at camp,

more than 60 years ago, and I loved it!

It was a tough game, because we had to skin

our own T. Rex and use his hide to make the ball

and his guts for the rope.