Question

A uniform metee rule rests horizontally on a knife edge at the 60 cm mark when a mass of 10 g is suspended from one end.

1)At which end must this mass be suspended?

2)What is the mass of the rule?

Answer 1

Knife edge is at 60 cm.
The mass "M" of the scale acts at 50 cm mark
The 10 g can be suspended at 0 mark or 100 mark.
Let us consider that the 0 mark is at the left.
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The question is, "At which end the mass is to be suspended?"
Assuming it is at 0 mark, and taking moments of the masses about the point 60 cm mark,
Both the moments of the mass 10g and M, are anticlockwise and hence the scale will not be balanced.
Hence the mass 10 g has to be suspended at the 100 cm mark.
Now taking moments about the point 60 cm,
The moment of 10 g is 10* 40 {since the distance between 60 cm mark and 100 cm mark is 40}. The direction is clockwise.
The moment of the mass M is M * 10 {since the distance between 60 cm mark and 50 cm mark is 10}. The direction is anticlockwise.

Equating the two, M*10 = 10* 40.
Hence the mass of the scale is 40 g,