Problem source

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The diagram shows a small railway wagon $A$ of mass $m$ standing
at the bottom of a smooth railway track of length $d$ inclined at
an angle $\theta$ to the horizontal. A light inextensible string,
also of length $d$, is connected to the wagon and passes over a light
frictionless pulley at the top of the incline. On the other end of
the string is a ball $B$ of mass $M$ which hangs freely. The system
is initially at rest and is then released. 

\begin{questionparts}

\item Find the condition which $m,M$ and $\theta$ must satisfy
to ensure that the ball will fall to the ground. Assuming that this
condition is satisfied, show that the velocity $v$ of the ball when
it hits the ground satisfies 
\[
v^{2}=\frac{2g(M-m\sin\theta)d\sin\theta}{M+m}.
\]

\item Find the condition which $m,M$ and $\theta$ must satisfy
if the wagon is not to collide with the pulley at the top of the incline.
\end{questionparts}