Answer
$B\lt C\lt A$
Work Step by Step
Initial acceleration for object A is given as
$a_A=\frac{F_A}{m_A}=\frac{11}{4}\frac{GM}{L^2}$
For object B
$a_B=\frac{F_B}{m_B}$
$a_B=\frac{\frac{4GM^2}{L^2}}{2M}$
$a_B=2\frac{GM}{L^2}$
For object C
$a_C=\frac{F_C}{m_C}$
$\implies a_C=\frac{27}{4}\frac{GM^2/L^2}{3M}$
$a_c=\frac{9}{4}\frac{GM}{L^2}$
Now we can rank the objects A, B and C in order of their increasing initial acceleration as follows:
$B\lt C\lt A$
