A60 n weight is suspended from one end of a 10 m wooden beam which weighs 30 n. where should the beam be picked up so that it balances?

The beam must be picked up at 8.33m respect to the opposite corner from the weight (to 1.66 m from the weight).

Explanation:

As we want the beam to be balanced, we will define the moment of the beam and the weight respect to an arbitrary point x from the opposite corner to the weight. The beam weight will be placed at the half of the beam:

(See the ilustration below to guide)

Where Wb and lb are the weight and the length of the beam.

Note that the zero distance from the picked-up force is due the force is located at the arbitrary point so no moment is doing.

Now due the beam has to be balanced the total moment must be zero:

Then is possible to find the x position point by solving the equation above:

For the respecting values:

real, smaller and upside-down.   so the answer should be b.

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