4. A light inextensible string of length \(l\) has one end attached to a fixed point \(A\). The other end is attached to a particle \(P\) of mass \(m\). The particle moves with constant speed \(v\) in a horizontal circle with the string taut. The centre of the circle is vertically below \(A\) and the radius of the circle is \(r\). Show that $$g r ^ { 2 } = v ^ { 2 } \sqrt { } \left( l ^ { 2 } - r ^ { 2 } \right) .$$