Question 2 - A-Level Maths

A particle P of mass 0.2 kg is connected to a fixed point O by a light inextensible string of length 3.2 m , and is moving in a vertical circle with centre O and radius 3.2 m . Air resistance may be neglected. When P is at the highest point of the circle, the tension in the string is 0.6 N .
1. Find the speed of P when it is at the highest point.
2. For an instant when OP makes an angle of \(60 ^ { \circ }\) with the downward vertical, find
  (A) the radial and tangential components of the acceleration of P ,
  (B) the tension in the string.
A solid cone is fixed with its axis of symmetry vertical and its vertex V uppermost. The semivertical angle of the cone is \(36 ^ { \circ }\), and its surface is smooth. A particle Q of mass 0.2 kg is connected to V by a light inextensible string, and Q moves in a horizontal circle at constant speed, in contact with the surface of the cone, as shown in Fig. 2. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5ecb198d-7863-4fc2-81b6-c8b6c37b1859-3_455_609_950_808} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure} The particle Q makes one complete revolution in 1.8 s , and the normal reaction of the cone on Q has magnitude 0.75 N .
1. Find the tension in the string.
2. Find the length of the string.