We have three force components to work with, and one moment.
The first step is to find equations that describe the components of force that are perpendicular to the beam, relative to the forces Fg, Fm and Ft
For Fg, the force component perpendicular to the beam will be Fg(cos(50)). Where Fg is the force due to the weight of the beam (350 kg) which is approximately 3500 N, given g = 10 m/s^2
For Fm, the force component perpendicular to the beam will be Fm(cos(50))
And finally for the tension force we have Ft(cos(40))
We can now use these forces to balance the moments around the hinge, where we need M1 to be zero
As torque is a function of both force and distance, we must multiply our perpendicular force components by the distance the force is acting from the hinge.
For the weight of the beam, the force acts through the center of mass, which will be at the center of the beam, so 2.1 m
For the tension force the distance will be 3 m
and for the Mass, the distance will be 4.2 m
We can now write an equation to balance the moments around the hinge.
As Fm and Fg are acing on an opposite side of the beam to Ft, Ft in our equation will be negative. In reality it doesn't matter if you take Ft as negative, or Fm and Fg as negative, as long as they are opposing.
This gives us the equation:
Fg(cos(50))(2.1) + Fm(cos(50))(4.2) - Ft(cos(40))(3) = M1
Where:
Fg = 3500 N
Ft = 1.3x10^4 N
M1 = 0 N m
We can now plug these values into the equation, and solve for Fm.
3500(cos(50))(2.1) + Fm(cos(50))(4.2) - (1.3x10^4)((cos(40))(3) = 0
4724.5 N + 2.7Fm N - 29875.7 N = 0
2.7*Fm N = 25151.2
Fm = 9315 N
This gives us a force in Newtons, but the questions asks for a Mass, Kg, so we just divide our answer by g = 10 to give our answer in Kg
931.3 Kg
Hope this helps