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A uniform disc of radius 45 cm has a circular hole of radius 15 cm cut out, so that the hole…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A uniform disc of radius $45\ \text{cm}$ has a circular hole of radius $15\ \text{cm}$ cut out, so that the hole touches the disc's edge. How far from the disc's centre is the centre of mass of what is left, and on which side?

Need a reminder? The key ideaShow

The centre of mass is the mass-weighted average position: $x_{cm} = \dfrac{\sum m_ix_i}{\sum m_i}$ , and the same for $y$ and $z$ . For a continuous body, $x_{cm} = \dfrac{\int x\,dm}{\int dm}$ . A hole can be treated as a negative mass.

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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