3
\includegraphics[max width=\textwidth, alt={}, center]{41b1f65b-8806-4183-81a1-0276691e203c-03_565_757_251_242}
The diagram shows a particle P , of mass 0.2 kg , which is attached by a light inextensible string of length 0.75 m to a fixed point O .
Particle P moves with constant angular speed \(\omega\) rads \(^ { - 1 }\) in a horizontal circle with centre vertically below O . The string is inclined at an angle \(\theta\) to the vertical.
The greatest tension that the string can withstand without breaking is 15 N .
- Find the greatest possible value of \(\theta\), giving your answer to the nearest degree.
- Determine the greatest possible value of \(\omega\).