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.

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Input the nearest integer to the minimum value of $1000 \mu$ as your answer.

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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.

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This is part of the set OCR A Level Problems .