a metre ruler balances itself at 58 cm mark when a weight of 20 gf is suspended from one end. what is tge weight of the metre ruler?
105 gf
A uniform metre rule
To find the weight of the meter ruler, we need to set up an equation based on the given information.
Let's assume the weight of the meter ruler is represented by W gf.
According to the information provided, when a weight of 20 gf is suspended from one end of the ruler, it balances at the 58 cm mark.
The weight of the ruler can be split into two components:
1. Weight due to the ruler's own mass, acting at the center.
2. Weight due to the suspended weight, acting at 58 cm mark.
Considering the lever principle, the clockwise moments (due to the suspended weight) must be equal to the anticlockwise moments (due to the weight of the ruler itself).
Since the center of the ruler is at the 50 cm mark (half of a meter), and it balances at the 58 cm mark, the distance between the center and the 58 cm mark is 8 cm.
Now, we can set up the equation:
(Weight of the ruler) × (distance from center to 58 cm mark) = (Weight of the suspended weight) × (distance from 58 cm mark to center)
Substituting the given values:
W × 8 cm = 20 gf × 8 cm
The distance from the 58 cm mark to the center cancels out on both sides of the equation, leaving us with:
W = 20 gf
Therefore, the weight of the meter ruler is 20 gf.
To find the weight of the meter ruler, we need to use the principle of moments. The principle of moments states that for an object to be in equilibrium, the sum of the clockwise moments about any point must be equal to the sum of the anticlockwise moments about the same point.
In this case, we can consider the pivot point to be the 58 cm mark, where the ruler balances. Let's assume that the length of the ruler is L and the weight of the ruler is W.
The clockwise moment is given by the weight of the ruler multiplied by the distance from the pivot point. Since the ruler balances at the 58 cm mark, the distance is (58 cm = 0.58 meters).
The anticlockwise moment is given by the weight of the 20 gf weight multiplied by the distance from the pivot, which is the length of the ruler (L) minus the distance from the pivot (0.58 meters). So, the anticlockwise moment is (20 gf * (L - 0.58 meters)).
According to the principle of moments, the clockwise moment must be equal to the anticlockwise moment: W * 0.58 meters = 20 gf * (L - 0.58 meters).
Now, we need to convert grams-force (gf) to kilograms-force (kgf) because weight is usually measured in kilograms.
1 kgf = 1000 gf.
So, the equation becomes: W * 0.58 meters = 0.02 kgf * (L - 0.58 meters).
To find the weight W of the ruler, we need to know the length L of the ruler. If you provide the length of the ruler, we can solve the equation to find the weight of the meter ruler.