Question

A uniform metre scale balances horizontally at the 44 cm mark when a weight of 20 g is placed at the 15 cm mark. What is the weight of the metre scale?

Answer 1

Given Data:

Length of metre scale = 100 cm

Position of fulcrum = 44 cm

Given weight (W₁) = 20 g at 15 cm mark

Weight of the scale (W) acts at its center of gravity = 50 cm mark

Distance from Fulcrum (44 cm):

Distance for 20 g weight (d₁) = 44 − 15 = 29 cm

Distance for scale’s weight (d₂) = 50 − 44 = 6 cm

According to the principle of moments:

Anticlockwise Moment = Clockwise Moment

W₁ × d₁ = W × d₂

20 × 29 = W × 6

580 = 6W

W = `580/6`

W = 96.67 g

W ≈ 97 g

The weight of the metre scale is 97 g.