Question

A uniform metre scale rests on a knife edge at the 60 cm mark. The scale becomes horizontal when a mass of 12 g is suspended from the one end of the scale. Which end of scale is this? What is the mass of the scale?

Answer 1

Given Data:

Length of metre scale = 100 cm

Position of knife edge (fulcrum) = 60 cm mark

Suspended mass (m) = 12 g

Mass of the scale (M) acts at its center of gravity = 50 cm mark

1. The weight of the scale (M) acts at the 50 cm mark, which is to the left of the fulcrum (60 cm). This creates an anticlockwise moment that tilts the left side of the scale down.

To balance the scale horizontally, the 12 g mass must be hung on the opposite side to create a clockwise moment.

Therefore, the mass is suspended from the right end (100 cm mark).

2. Distance from Fulcrum (60 cm):

Distance for mass of the scale (d₁) = 60 − 50 = 10 cm

Distance for 12 g suspended mass (d₂) = 100 − 60 = 40 cm

According to the principle of moments:

Anticlockwise Moment = Clockwise Moment

M × d₁ = m × d₂

M × 10 = 12 × 40

10 M = 480

M = `480/10`

M = 48 g