Torque and Equilibrium question

[SPCPhysicss]

Homework Statement

A uniform wooden board of mass 10 M is held up by a nail hammered into a wall. A block of mass M rests L/2 away from the pivot. Another block of a certain mass (?) is hung a distance L/3. The system is in static equilibrium.

What is the measure of the mass labeled "?"

Homework Equations

T=(D)(F)

The Attempt at a Solution

I know that the answer is 3M/2, but I just cannot find the thought process behind the answer. I tried to set up an equation so that T=(M)(L/2)= (M)(L/3), to try and find the answer, but obviously it isn't correct. Could I use imaginary numbers for the Mass and the length to find a fake torque then find the mass when it's at equilibrium?

Please, someone help me at least get started, I really need the help

 

[cupid.callin]

write the two torque acting on pivot due to two masses

 

[SPCPhysicss]

Sorry, but I don't really understand what you mean. Do I need to set them equal to each other?


So I tried to substitute in fake values and when I found both the torques, they equalled each other. I think I have the right work, but I thought that if the mass was closer to the center of mass it needed more torque.

 

[cupid.callin]

Yes you need to equate them

If Στ=0 then α=0
which means that body is in rotational equilibrium

but I thought that if the mass was closer to the center of mass it needed more torque.

I can't understand you.

 

[SPCPhysicss]

Hmm I see, so the equation I should write would look like,

(Mg)(L/2)=x(L/3)?

I don't quite know what to do from there I assume you need to divide by a 2? and then somehow multiply the Mass by 3?

 

[cupid.callin]

You wrote the eqn correct

Now just cancel L and take 3 to other side and you'll get ? = 3M/2