Challenging +1.8 This is a challenging M5 question requiring conservation of angular momentum about a fixed axis, relating linear and angular velocities at the impact point, and finding the moment of inertia of a rod about an off-center point using the parallel axis theorem. It demands careful setup of multiple equations and algebraic manipulation, going beyond routine collision problems but following standard M5 techniques.
2. A rod \(A B\) has mass \(m\) and length \(4 a\). It is free to rotate about a fixed smooth horizontal axis through the point \(O\) of the rod, where \(A O = a\). The rod is hanging in equilibrium with \(B\) below \(O\) when it is struck by a particle \(P\), of mass \(3 m\), moving horizontally with speed \(v\). When \(P\) strikes the rod, it adheres to it. Immediately after striking the rod, \(P\) has speed \(\frac { 2 } { 3 } v\).
Find the distance from \(O\) of the point where \(P\) strikes the rod.
(7 marks)
2. A rod $A B$ has mass $m$ and length $4 a$. It is free to rotate about a fixed smooth horizontal axis through the point $O$ of the rod, where $A O = a$. The rod is hanging in equilibrium with $B$ below $O$ when it is struck by a particle $P$, of mass $3 m$, moving horizontally with speed $v$. When $P$ strikes the rod, it adheres to it. Immediately after striking the rod, $P$ has speed $\frac { 2 } { 3 } v$.
Find the distance from $O$ of the point where $P$ strikes the rod.\\
(7 marks)\\
\hfill \mbox{\textit{Edexcel M5 Q2 [7]}}