A particle \(P\) of mass 0.5 kg is attached to one end of a light inextensible string of length 1.5 m . The other end of the string is attached to a fixed point \(A\). The particle is moving, with the string taut, in a horizontal circle with centre \(O\) vertically below \(A\). The particle is moving with constant angular speed \(2.7 \mathrm { rad } \mathrm { s } ^ { - 1 }\). Find
- the tension in the string,
- the angle, to the nearest degree, that \(A P\) makes with the downward vertical.
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A child's toy consists of a uniform solid hemisphere, of mass \(M\) and base radius \(r\), joined to a uniform solid right circular cone of mass \(m\), where \(2 m < M\). The cone has vertex \(O\), base radius \(r\) and height \(3 r\). Its plane face, with diameter \(A B\), coincides with the plane face of the hemisphere, as shown in Figure 1.