A particle $P$ of mass $0.4{\text{ }}kg$ is attached to a fixed point $A$ by a light inextensible string. The string is inclined at ${60^ \circ }$ to the vertical. $P$ moves with constant speed in a horizontal circle of radius $0.2{\text{ }}m$. The centre of the circle is vertically below $A$ (see diagram).
a) Show that the tension in the string is $8{\text{ }}N$.
b) Calculate the speed of the particle.

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