1 A particle \(P\) of mass 0.3 kg moves in a circle with centre \(O\) on a smooth horizontal surface. \(P\) is attached to \(O\) by a light elastic string of modulus of elasticity 12 N and natural length \(l \mathrm {~m}\). The speed of \(P\) is \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), and the radius of the circle in which it moves is \(2 l \mathrm {~m}\). Calculate \(l\).