Show that \(\mathrm { x } = \frac { 32 \mathrm { a } ^ { 2 } + 3 \mathrm { ad } } { 16 \mathrm { a } + 3 \mathrm {~d} }\) and find an expression, in terms of \(a\) and \(d\), for \(\bar { y }\).
The object is placed on a rough plane which is inclined to the horizontal at an angle \(\theta\) where \(\sin \theta = \frac { 1 } { 6 }\). The object is in equilibrium with \(C O\) horizontal, where \(C O\) lies in a vertical plane through a line of greatest slope.