A stone of mass $500$g is attached to a string of length $50$cm which will break if the tension in it exceeds $20$N. The stone is whirled in a vertical circle, the axis of rotation being at a height of $100$cm above the ground. The angular speed is very slowly increased until the string breaks. In what position is this break most likely to occur, and at what angular speed? Where will the stone hit the ground?

My attempt :

Here, mass of stone (m)=$0.5$kg

Length of string (l)=$0.5$m

Height above the ground (h')=$1$m

Let, $\omega $ be the angular speed when the stone breaks.

Then maximum tension in string =$m\omega^2 r+mg$

$$20=0.5\times \omega^2 \times 0.5+10$$

$$\omega =7.75 \textrm {rads^-1}$$