Problem source

Two particles, $A$ and $B$,  of masses $m$ and $2m$,
respectively, are placed on a line of greatest slope, $\ell$, of a 
rough inclined plane which makes
an angle of $30^{\circ}$ with the horizontal. The coefficient
of friction between $A$ and the plane is $\frac16\sqrt{3}$ 
and the coefficient of 
friction between $B$ and the plane is $\frac13 \sqrt{3}$. 
The particles  are at rest with
$B$ higher up $\ell$ than $A$ and are connected by a light inextensible string 
which is taut. A force $P$ is applied to $B$.
\begin{questionparts}
\item Show that the least magnitude of $P$ for which 
the two particles move upwards along $\ell$ is 
$\frac{11}8 \sqrt{3}\, mg$ and give, in this case,
 the direction in which $P$ acts.
\item Find the least magnitude of $P$ for which the particles
do not slip downwards along~$\ell$.
\end{questionparts}