6. \begin{figure}[h] \end{figure} A small smooth ring \(R\) of mass \(m\) is threaded on to a smooth wire in the shape of a circle with centre 0 and radius \(I\). The wire is fixed in a vertical plane. The ring \(R\) is attached to one end of a light elastic string of natural length I and modulus of elasticity mg . The other end of the elastic string is attached to A , the lowest point of the wire. The point B is on the wire and \(O B\) is horizontal. The ring \(R\) is at rest at the highest point of the wire, as shown in Figure 6.
The ring \(R\) is slightly disturbed from rest and slides along the wire.
At the instant when \(R\) reaches the point \(B\), the speed of \(R\) is \(v\) and the magnitude of the force exerted on R by the wire is N .

1. Show that $$v ^ { 2 } = 2 g l \sqrt { 2 }$$
2. Show that $$N = \frac { 1 } { 2 } m g ( 5 \sqrt { 2 } - 2 )$$
   \(\_\_\_\_\) VIAV SIHI NI JIIHM ION OC
   VILU SIHIL NI GLIUM ION OC
   VEYV SIHI NI ELIUM ION OC