7 A uniform solid hemisphere has radius 0.4 m . A uniform solid cone, made of the same material, has base radius 0.4 m and height 1.2 m . A solid, \(S\), is formed by joining the hemisphere and the cone so that their circular faces coincide. \(O\) is the centre of the joint circular face and \(V\) is the vertex of the cone. \(G\) is the centre of mass of \(S\).

1. Explain briefly why \(G\) lies on the line through \(O\) and \(V\).
2. Show that the distance of \(G\) from \(O\) is 0.12 m .
   (The volumes of a hemisphere and cone are \(\frac { 2 } { 3 } \pi r ^ { 3 }\) and \(\frac { 1 } { 3 } \pi r ^ { 2 } h\) respectively.)
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   \(S\) is suspended from two light vertical strings, one attached to \(V\) and the other attached to a point on the circumference of the joint circular face, and hangs in equilibrium with OV horizontal (see diagram).
3. The weight of \(S\) is \(W\). Find the magnitudes of the tensions in the strings in terms of \(W\).