Is net torque is not zero about all points on the rod for a linearly accelerating rod?

Question

Consider thin uniform rod $AB$ of mass $m$ and length $L$ just translating with some acceleration $a$ due to two anti parallel forces $F_1$ and $F_2$ perpendicular to the rod. Force $F_1$ acts at the end $A$ where as $F_2$ acts at distance $y$ from end $A$.

Because body is just translating, Net torque on the body about any point on the rod be zero.

About Center of Mass:

$F_1.L/2 = F_2.(L/2-y)$ gives me a ratio of $F1/F2$

If I proceed with these values of F1 and F2 then net torque about the end B is not zero.

About end B of the rod:

$F_1.L = F_2.(L-y)$ gives me another value for $F1/F2$

If I proceed with these values of F1 and F2 then net torque about the center of mass is not zero.

Where am I going wrong?

EDIT: I have generalized the above situation from the following problem:

Solution to the above problem says "Since the rod moves translationally only, Hence Torque about $B$ is zero. Hence $N = 0$ and hence $x=2$"

Answer 1

EDIT-

I would like to tell that there was a flaw in my last answer.

Because body is just translating, Net torque on the body about any point on the rod be zero.

My previous answer told that this was wrong. This is indeed correct.

As the rod moves in a straight line, the acceleration of every point on the will be $2m/s^2$. If you want to balance the torque about $B$, you must add the pseudo force on the COM as point $B$ is accelerating with $2m/s^2$ too!

If you do that, you will get the same value for $\frac{F_1}{F_2}$.

Here in this photograph I have taken the general case which proves that torque about any point is zero which indeed gives us the same value of $\frac{F_1}{F_2}$

Answer 2

Update as a result of more information being given in the question

The rod is subjected to a net force at its centre of mass of $F_2-F_1$ to the right and an anticlockwise couple of $(F_1-F_2)\dfrac L2 + F_2y$ as shown in the diagram below.

The magnitude (and direction) of the couple is independent of the point about which you measure the couple so if the bar is undergoing only translation the magnitude of the couple must be zero which gives $F_1=3\,\rm N$.
From that you can work out the torque about $B$ and hence find a value for $x$.