1.
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\caption{Figure 1}
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A hollow right circular cone, of base radius \(a\) and height \(h\), is fixed with its axis vertical and vertex downwards, as shown in Figure 1. A particle moves with constant speed \(v\) in a horizontal circle of radius \(\frac { 1 } { 3 } a\) on the smooth inner surface of the cone.
Show that \(v = \sqrt { } \left( \frac { 1 } { 3 } h g \right)\).