Fig. 2 shows a hollow cone mounted with its axis of symmetry vertical and its vertex V pointing downwards. The cone rotates about its axis with a constant angular speed of \(\omega \mathrm { rad } \mathrm { s } ^ { - 1 }\). A particle P of mass 0.02 kg is in contact with the rough inside surface of the cone, and does not slip. The particle P moves in a horizontal circle of radius 0.32 m . The angle between VP and the vertical is \(\theta\).
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\caption{Fig. 2}
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In the case when \(\omega = 8.75\), there is no frictional force acting on P .
- Show that \(\tan \theta = 0.4\).
Now consider the case when \(\omega\) takes a constant value greater than 8.75.
- Draw a diagram showing the forces acting on P .
- You are given that the coefficient of friction between P and the surface is 0.11 . Find the maximum possible value of \(\omega\) for which the particle does not slip.