Question

A uniform metre scale of mass 70 g is suspended from the 65 cm mark on the scale. Where should a 50 g mass be suspended on the scale to keep the scale in the horizontal position?

Answer 1

Given:

Mass of the metre scale (M) = 70 g

Position of center of gravity = 50 cm

Position of pivot (suspension point) = 65 cm

Mass to be suspended (m) = 50 g

Calculation:

Distance of scale’s mass from pivot (d₁) = 65 cm − 50 cm = 15 cm (Anticlockwise side)

Let the distance of 50 g mass from pivot be d₂ (Clockwise side)

According to the Principle of Moments:

Anticlockwise Moment = Clockwise Moment

M × d₁ = m × d₂

70 × 15 = 50 × d₂

1050 = 50 × d₂

d₂ = `1050/50`

d₂ = 21 cm

Position on the scale:

Mark on scale = 65 cm + 21 cm = 86 cm

The 50 g mass should be suspended at the 86 cm mark.