7 A particle \(P\) of mass 0.7 kg is attached to one end of a light inextensible string of length 0.5 m . The other end of the string is attached to a fixed point \(A\) which is \(h \mathrm {~m}\) above a smooth horizontal surface. \(P\) moves in contact with the surface with uniform circular motion about the point on the surface which is vertically below \(A\).

1. Given that \(h = 0.14\), find an inequality for the angular speed of \(P\).
2. Given instead that the magnitude of the force exerted by the surface on \(P\) is 1.4 N and that the speed of \(P\) is \(2.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), calculate the tension in the string and the value of \(h\).