Question

A uniform metre scale is balanced at 40 cm mark, when weights of 25 gf and 10 gf are suspended at 5 cm mark and 75 cm mark respectively. Calculate weight of the metre scale.

Answer 1

As metre scale is uniform, therefore its weight acts at 50 cm mark.

Taking moments about 40 cm mark.

Moment in clockwise direction = W × 10 cm + 10 gf × 35 cm = 10 W cm + 350 gfcm

Moment in anticlockwise direction = 25 gf × 35 cm = 875 gfcm

By the law of moments,

Moment in clockwise direction = Moment in anticlockwise direction.

10 W cm + 350 gfcm = 875 gfcm

∴ 10 W cm = (875 − 350) gfcm

\[\text{W} = \frac{525}{10}\text{gf}\]

= 52.5 gf