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Nov 2015 p51 q3
One end of a light inextensible string is attached to a fixed point \( A \) and the other end of the string is attached to a particle \( P \). The particle \( P \) moves with constant angular speed \( 5 \,\text{rad s}^{-1} \) in a horizontal circle which has its centre \( O \) vertically below \( A \). The string makes an angle \( \theta \) with the vertical (see diagram). The tension in the string is three times the weight of \( P \).
(i) Show that the length of the string is \( 1.2 \) m. \(\quad [3] \)
(ii) Find the speed of \( P \). \(\quad [4] \)
