5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e0668f31-4b72-4dfd-9cf7-470acef0bfdb-4_693_554_196_717}
\captionsetup{labelformat=empty}
\caption{Fig. 3}
\end{figure}
A flask is modelled as a uniform solid formed by removing a cylinder of radius \(r\) and height \(h\) from a cylinder of radius \(\frac { 4 } { 3 } r\) and height \(\frac { 3 } { 2 } h\) with the same axis of symmetry and a common plane as shown in Figure 3.
- Show that the centre of mass of the flask is a distance of \(\frac { 9 } { 10 } h\) from the open end of the flask.
The flask is made from a material of density \(\rho\) and is filled to the level of the open plane face with a liquid of density \(k \rho\). Given that the centre of mass of the flask and liquid together is a distance of \(\frac { 15 } { 22 } h\) from the open end of the flask,
- find the value of \(k\).
- Explain why it may be advantageous to make the base of the flask from a more dense material.
(2 marks)