A uniform metre scale is in equilibrium as shown in the diagram :
Calculate the weight of the metre scale.
Topic: Force, moments and circular motion
Answer
From the diagram, taking moments about the fulcrum: the 40 gf weight acts 25 cm from the fulcrum, the weight of the scale W acts at its centre, 20 cm from the fulcrum on the other side.
A uniform metre scale has its whole weight acting at its mid-point, the 50 cm mark.
By the principle of moments, for equilibrium: anticlockwise moment = clockwise moment 40 × 25 = W × 20 1 000 = 20W W = 1 000 ÷ 20 W = 50 gf
Weight of the metre scale = 50 gf
The key idea is that a UNIFORM scale behaves as though its entire weight is concentrated at its centre of gravity, the 50 cm mark. That is the only reason the problem has a single force to balance rather than a spread-out weight.
Moment = force × PERPENDICULAR DISTANCE FROM THE FULCRUM — not from the end of the scale, and not the position mark itself. Read the distance off the diagram as a gap between two points, and if the fulcrum is at the 30 cm mark and the weight hangs at 5 cm, the distance is 25 cm, not 5.
Both sides are in gf, so there is no need to convert to newtons — the units cancel in the balance.