5 A particle, of mass 6 kg , is attached to one end of a light inextensible string. The other end of the string is attached to the fixed point \(O\). The particle is set in motion, so that it moves in a horizontal circle at constant speed, with the string at an angle of \(30 ^ { \circ }\) to the vertical. The centre of this circle is vertically below \(O\).
\includegraphics[max width=\textwidth, alt={}, center]{851cb2a3-5bc8-4af9-b1fc-a143d37beebe-4_586_490_541_767} The particle moves in a horizontal circle with an angular speed of 40 revolutions per minute.

1. Show that the angular speed of the particle is \(\frac { 4 \pi } { 3 }\) radians per second.
2. Show that the tension in the string is 67.9 N , correct to three significant figures.
3. Find the radius of the horizontal circle.