# OCR A Level: Mechanics 2 - Centre Of Mass [January 2011 Q5]

**Classical Mechanics**Level 5

A uniform solid is made of a hemisphere with centre \(O\) and radius \(0.6\text{ m}\), and a cylinder of radius \(0.6\text{ m}\) and height \(0.6\text{ m}\). The plane face of the hemisphere and a plane face of the cylinder coincide.

\(\text{(i)}\) Show that the distance of the centre of mass of the solid from \(O\) is \(0.09\text{ m}\).

\(\text{(ii)}\) The solid is placed with the curved surface of the hemisphere on a rough horizontal surface and the axis inclined at \(45^\circ \) to the horizontal. The equilibrium of the solid is maintained by a horizontal force of \(2N\) applied to the highest point on the circumference of its plane face. Calculate

\(\textbf{(a)}\) the mass of the solid,

\(\textbf{(b)}\) the set of possible values of the coefficient of friction, \(\mu \), between the surface and the solid.

**Input the nearest integer to the minimum value of \(1000 \mu \) as your answer.**