Answer
$A \lt B \lt C$
Work Step by Step
The gravitational force on object A is given as
$F_A=\frac{GM(2M)}{L^2}+\frac{GM(3M)}{(2L)^2}=\frac{11}{4}\frac{GM^2}{L^2}$
For object B
$F_B=\frac{GM(2M)(3M)}{L^2}+\frac{GM(2M)}{(L)^2}=4\frac{GM^2}{L^2}=\frac{16}{4}\frac{GM^2}{L^2}$
For object C
$F_C=\frac{G(3M)(2M)}{L^2}+\frac{GM(3M)}{(2L)^2}=4\frac{GM^2}{L^2}=\frac{27}{4}\frac{GM^2}{L^2}$
Now, we can rank A, B and C in order of increasing gravitational force as
$A \lt B \lt C$
