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

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.

×