Find \(r\).
The upper cylinder is now fixed to the lower cylinder to create a uniform object.
Show that the centre of mass of the object is
$$\frac { 25 h ^ { 2 } + 180 h + 81 } { 50 h + 180 } \mathrm {~m}$$
from \(A\).
The object is placed with the plane face containing \(A\) in contact with a rough plane inclined at \(\alpha ^ { \circ }\) to the horizontal, where \(\tan \alpha = 0.5\). The object is on the point of toppling without sliding.