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

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SUMMARY

The optimal placement for support A in the torque problem involving a 1.0-m-long nonuniform plank weighing 1000 N is determined by analyzing the torques around support B, which is positioned 10 cm from the right edge. Given that the center of mass is 30 cm from the right edge and each support bears half the weight (500 N), the calculation reveals that support A should be placed 50 cm from the left-hand edge. This conclusion is reached by applying the principle of torque equilibrium, where the clockwise torque equals the counterclockwise torque.

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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.
 

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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.
 
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?
 

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