What is the optimal placement for support A in this torque problem?

[apphysicsgirl]

1. The 1.0-m-long nonuniform plank has weight 1000 N. It is supported by two rods, A and B, as shown above. The center of mass of the plank is 30 cm from the right edge. Each support bears half the weight of the plank. If support B is 10 cm from the right-hand edge, how far from the left-hand edge should support A be?

The attached image is the picture for this problem that was given.



2. torque (clockwise)=torque (counterclockwise)
torque=Fr



3. This is a multiple choice question and the choices are : 0 cm, 10 cm, 30 cm, 50 cm, and 70 cm. I have no idea how to do this problem so help would be appreciated.

 

[PhanthomJay]

The support forces are given as 500 N each. So just use your equation to solve, by summing torques about the right support. Be sure to draw a sketch properly showing all dimensions.

 

[Adjuster]

Do you think the questioner could expect a student to solve this problem mentally? When you've solved the problem formally, look for a simpler way of getting the same result.
Hint - when the support forces are equal, how far is the centre of mass from each support?