Torque and Force question -- Multipe forces acting on an object

[shivam2571]

Homework Statement

The resultant of two unlike parallel forces is10N and acts at a distance of 35cm and 45cm from them. The forces are:

Relevant Equations

F1.d1=F2.d2 (d is perpendicular distance of Axis of rotation to line of action)
F1-F2=10 (since forces are unlike and parallel)

I have attempted and got 2 different solution
1:

2:

 

[Lnewqban]

Welcome!
What about the moments?
Is there equilibrium of moments in the system?

 

[kuruman]

There seems to be a contradiction in what you posted. The resultant is the vector sum of two forces. If the forces are parallel, the resultant is the sum of the magnitudes. You use the difference of the magnitudes to denote the resultant. That to be correct if the forces are antiparallel, i.e. point in opposite directions. Which is it, parallel or antiparallel?

Better yet, please post the problem statement exactly as was given to you.

 

[haruspex]

There seems to be a contradiction in what you posted. The resultant is the vector sum of two forces. If the forces are parallel, the resultant is the sum of the magnitudes. You use the difference of the magnitudes to denote the resultant. That to be correct if the forces are antiparallel, i.e. point in opposite directions. Which is it, parallel or antiparallel?

Better yet, please post the problem statement exactly as was given to you.

I think the OP is using "unlike" to mean opposite directions.

 

[haruspex]

I have attempted and got 2 different solution
1:

2:

In your second solution, your force balance equation assumes the resultant acts in the same direction as as F₁, but your torque balance equation assumes it acts in the same direction as F₂.
The diagram places the resultant between the two forces. If that were so, taking moments about a point in its line could not produce zero. Had you been consistent in your two equations, I expect you would have got a negative value for one of the forces.

 

[kuruman]

I think the OP is using "unlike" to mean opposite directions.

I took to mean unequal but I can see the interpretation with a hyphen as in unlike-parallel. In any case without a clear statement of the problem as given to OP, one can only guess what it could be. It looks like quite a bit has been lost in translation.