Standard +0.3 This is a standard circular motion problem on a conical surface requiring resolution of forces (normal reaction, weight) perpendicular and parallel to the surface, use of F=mrω², and geometric relationships. While it involves multiple steps and careful geometry (finding the cone's semi-vertical angle from dimensions, relating radius to height), it follows a well-established template for M3 conical pendulum problems with no novel insight required. The 11 marks reflect length rather than conceptual difficulty.
\includegraphics{figure_1}
A hollow cone, of base radius \(3a\) and height \(4a\), is fixed with its axis vertical and vertex \(V\) downwards, as shown in Figure 1. A particle moves in a horizontal circle with centre \(C\), on the smooth inner surface of the cone with constant angular speed \(\sqrt{\frac{8g}{9a}}\).
Find the height of \(C\) above \(V\).
[11]
\includegraphics{figure_1}
A hollow cone, of base radius $3a$ and height $4a$, is fixed with its axis vertical and vertex $V$ downwards, as shown in Figure 1. A particle moves in a horizontal circle with centre $C$, on the smooth inner surface of the cone with constant angular speed $\sqrt{\frac{8g}{9a}}$.
Find the height of $C$ above $V$.
[11]
\hfill \mbox{\textit{Edexcel M3 2006 Q4 [11]}}