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A small ball \(B\) of mass 0.5 kg moves in a horizontal circle with centre \(O\) and radius 0.4 m on the smooth inner surface of a hollow cone fixed with its vertex down. The axis of the cone is vertical and the semi-vertical angle is \(60 ^ { \circ }\) (see diagram).
- Show that the magnitude of the force exerted by the cone on \(B\) is 5.77 N , correct to 3 significant figures, and calculate the angular speed of \(B\).
One end of a light elastic string of natural length 0.45 m and modulus of elasticity 36 N is attached to \(B\). The other end of the string is attached to the point on the axis 0.3 m above \(O\). The ball \(B\) again moves on the surface of the cone in the same horizontal circle as before.
- Calculate the speed of \(B\).