Problem source

$\ $\vspace{-1cm}
	
	\noindent
	\begin{center}
		\psset{xunit=1.0cm,yunit=1.0cm,algebraic=true,dotstyle=o,dotsize=3pt 0,linewidth=0.5pt,arrowsize=3pt 2,arrowinset=0.25}
		\begin{pspicture*}(-3.18,-6.26)(2.72,2.3)
		\pscircle(0,0){2}
		\psline[linewidth=1.2pt](-2,0)(-2,-4)
		\psline[linewidth=1.2pt](2,0)(2,-5)
		\rput[tl](-2.5,0.14){$R$}
		\rput[tl](0.2,0.2){$O$}
		\rput[tl](2.2,0.14){$Q$}
		\rput[tl](-2.1,-4.26){$S$}
		\rput[tl](1.86,-5.2){$P$}
		\parametricplot[linewidth=1.2pt]{0.0}{3.141592653589793}{1*2*cos(t)+0*2*sin(t)+0|0*2*cos(t)+1*2*sin(t)+0}
		\begin{scriptsize}
		\psdots[dotstyle=+,dotsize=6pt](0,0)
		\end{scriptsize}
		\end{pspicture*}
		\end{center}
		
		
A uniform circular disc with  radius $a$, mass $4m$ and centre $O$ is freely
mounted on a fixed horizontal axis which is
perpendicular to its plane and passes through $O$. A uniform heavy chain
$PS$ of length $(4+\pi)a$, mass $(4+\pi)m$ and negligible thickness is
hung over the rim of the disc as shown in the diagram: $Q$ and $R$ are
the points of the chain at the same level as $O$. The contact between the
chain and the rim of the disc is sufficiently rough to prevent slipping.
Initially, the system is at rest with $PQ=RS =2a$. A particle of mass 
$m$ is attached to the chain at $P$ and the system is released. 
By considering the energy of the system, show that when $P$ has descended
a distance $x$, its speed $v$ is given by
$$
(\pi+7)av^2 = 2g(x^2+ax).
$$
By considering the part $PQ$ of the chain as a body of variable mass, show 
that when $S$ reaches $R$ the tension in the chain at $Q$ is
$$
{5\pi -2 \over \pi +7} mg.
$$