.A uniform metre rule balances horizontally on a knife edge placed at the 58 cm mark when a weight of 20gf is suspended from one end. what is the weight of the rule? *
The mass of the rule acts at the 50cm mark (8cm from the fulcrum), so
8m = 20*42
m = 105g
To determine the weight of the rule, we need to use the principle of moments. The principle of moments states that for an object in equilibrium, the sum of the clockwise moments about any point is equal to the sum of the anticlockwise moments about the same point.
In this situation, we have a uniform meter rule balanced on a knife edge placed at the 58 cm mark. Let's assume that the weight of the rule is Wg.
Now, considering the clockwise and anticlockwise moments, we can write:
Clockwise moment = Weight of the rule (Wg) × Distance of the knife edge from the weight
Anticlockwise moment = 20 gf (weight) × Distance of the weight from the knife edge
Since the rule is balanced, the clockwise moment is equal to the anticlockwise moment. In equation form:
Wg × Distance of the knife edge from the weight = 20 gf × Distance of the weight from the knife edge
Since the distance of the knife edge from the weight is given as 58 cm, and the distance of the weight from the knife edge is 100 cm (assuming the rule is 100 cm in total length), we can substitute these values into the equation:
Wg × 58 cm = 20 gf × 100 cm
Simplifying the equation:
Wg = (20 gf × 100 cm) / 58 cm
Wg ≈ 34.5 gf
Therefore, the weight of the rule is approximately 34.5 gf.