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.

There are 5 marks available for part (i), 4 marks for part (ii) (a) and 3 marks for part (ii) (b).
In total, this question is worth 16.7% of all available marks in the paper.

This is part of the set OCR A Level Problems.

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