OCR MEI Further Mechanics Minor 2019 June — Question 3

Exam BoardOCR MEI
ModuleFurther Mechanics Minor (Further Mechanics Minor)
Year2019
SessionJune
TopicCentre of Mass 1

3 Two identical uniform rectangular laminas, P and Q , each having length \(k a\) and width \(a\) are fixed together, in the same plane, to form a lamina R.
With reference to coordinate axes, the corners of P are at ( 0,0 ), ( \(k a , 0\) ), ( \(k a , a\) ) and ( \(0 , a\) ) and the corners of Q are at \(( k a , 0 ) , ( k a + a , 0 ) , ( k a + a , k a )\) and \(( k a , k a )\), as shown in Fig. 3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3b808042-95b8-4862-8355-3979c1981089-3_704_1102_459_244} \captionsetup{labelformat=empty} \caption{Fig. 3}
\end{figure} Determine the range of values of \(k\) for which the centre of mass of R lies outside the boundary of R.