Calculate the block mass in an equilibrium system with two supports

[hidemi]

Homework Statement

Two supports, made of the same material and initially of equal length, are 2.0 m apart. A stiff board with a length of 4.0 m and a mass of 10 kg is placed on the supports, with one support at the left end and the other at the midpoint. A block is placed on the board a distance of 0.50 m from the left end. As a result the board is horizontal (that is, the downward force on each support is the same). The mass of the block is:

A. zero
B. 2.3 kg
C. 6.6 kg
D. 10 kg
E. 20 kg

ans: E

Relevant Equations

F = ma
T = r x F

The attachment is the key. I wonder where the (3/8)L comes from. Can someone explain it, please? Thanks.

 

[haruspex]

The 10kg mass is 3/8 L from the centre of the board.
But the easiest way to solve it is to take moments about a point 1m from the left end. The two normal forces cancel.

 

[hidemi]

I wonder why you take the moments about 1m from the left end?

 

[haruspex]

I wonder why you take the moments about 1m from the left end?

So that the torques of the two normal forces cancel.

 

[hidemi]

So that the torques of the two normal forces cancel.

I see, thank you.