A body of mass 120g placed at the 10cm mark on a uniform metre rule makes the rule settle horizontally on a fulcrum places at 35cm mark. Calculate the mass of the rule

Rityxtar

3 years ago

25 is gotten from 35-10 while 15 is gotten from 50-35 the weight of the metre rule acts at its centre of gravity

kecyfrancis

10 years ago

sorry how did you get the 15 and the 25

young123richie

1 year ago

To solve this problem, we can use the principle of moments. Let's denote the mass of the rule as M.

Given Information
1. Mass of the body (m) = 120 g = 0.12 kg (converting to kg for consistency)
2. Position of the body = 10 cm mark
3. Fulcrum position = 35 cm mark

Calculating the Mass of the Rule
Since the rule is uniform, its center of gravity is at the 50 cm mark (midpoint of a 1-meter rule).

Let's denote the distance from the fulcrum to the center of gravity of the rule as d₁ and the distance from the fulcrum to the body as d₂.

d₁ = 50 cm - 35 cm = 15 cm = 0.15 m
d₂ = 35 cm - 10 cm = 25 cm = 0.25 m

Using the principle of moments:

M × g × d₁ = m × g × d₂

where g is the acceleration due to gravity (approximately 9.8 m/s²). Since g is present on both sides, it cancels out:

M × 0.15 = 0.12 × 0.25

M = (0.12 × 0.25) / 0.15
M = 0.2 kg or 200 g

The mass of the rule is 200 g.