Question 7.4
A mass $m_1$ is joined to a massless, frictionless, movable pulley with a massless,
inextensible string, through another pulley that hangs from a fixed support.
Two masses $m_2$ and $m_3$ are joined by a massless, inextensible string that
wraps around the movable pulley.
(a) Find a condition on the three masses $m_1$, $m_2$ and $m_3$ where all of them
are in equilibrium.
(b) Show that the mass $m_1$ remains in equilibrium under gravity, provided
that
$m_1 = \frac{4m_2m_3}{m_2 + m_3}$.
(7.4.1)
Under the condition in equation (7.4.1) only, while the mass $m_1$ remains sta-
tionary, the masses $m_2$ and $m_3$ are allowed to accelerate.
Hint: You are not required to find the accelerations in the general case. You
can directly determine the tensions in the strings by the equilibrium assump-
tions.