Question

A uniform metre scale is balanced at 60 cm mark, when weights of 5 gf and 40 gf are suspended at 10 cm mark and 80 cm mark respectively. Calculate the weight of the metre scale.

Answer 1

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

Taking moments about 60 cm mark.

Moment in clockwise direction = 40 gf × 20 cm = 800 gfcm

Moment in anticlockwise direction = W × 10 cm + 5 gf × 50 cm = 10 W cm + 250 gfcm

By the law of moments,

Moment in clockwise direction = Moment in anticlockwise direction.

10 W cm + 250 gfcm = 800 gfcm

∴ 10 W cm = (800 − 250) gfcm

\[ \therefore \text{W} = \frac{550}{10}\ \text{gf} \]

= 55 gf