Answer
The net gravitational force on the central sphere is zero.
Work Step by Step
In part (a), we found that $M = m$
We can let the mass of the central sphere be $2~m_4$
By symmetry, the horizontal component of the net gravitational force on the central sphere is zero.
Let the distance from the central sphere to the other spheres be $d$
We can find the vertical component of the net gravitational force on the central sphere:
$F_y = \frac{G~M~(2~m_4)}{d^2} - 2 \times\frac{G~m~(2~m_4)}{d^2}~sin~30^{\circ}$
$F_y = \frac{G~M~(2~m_4)}{d^2} - \frac{G~m~(2~m_4)}{d^2}$
$F_y = \frac{G~m~(2~m_4)}{d^2} - \frac{G~m~(2~m_4)}{d^2}$
$F_y = 0$
The net gravitational force on the central sphere is zero.
