A uniform meter rule AB is balance on a knife edge which is 55cm from B, if a mass of 10g is hung at P which is 10cm from A calculate the mass of the meter rule
To calculate the mass of the meter rule, we can make use of the principle of moments. The principle of moments states that if an object is in rotational equilibrium, the sum of the clockwise moments is equal to the sum of the anticlockwise moments.
Given:
Distance from the knife edge to point B (55 cm)
Distance from point P to point A (10 cm)
Mass hanging at point P (10 g)
Let's assume the mass of the meter rule is "M" grams.
The clockwise moment is given by the product of the mass and the distance from the knife edge, while the anticlockwise moment is given by the product of the hanging mass and its distance from point A.
Clockwise moment = M × 55 cm
Anticlockwise moment = 10 g × 10 cm
Since the meter rule is balanced (no net rotation), the clockwise moment is equal to the anticlockwise moment:
M × 55 cm = 10 g × 10 cm
To solve for M, let's convert the units to a consistent form. Since 1 g = 0.001 kg and 1 cm = 0.01 m:
M × 0.55 m = 0.01 kg × 0.1 m
Simplifying the equation:
M = (0.01 kg × 0.1 m) / 0.55 m
M = 0.001 kg / 0.55
M ≈ 0.0018 kg (or 1.8 grams)
Therefore, the mass of the meter rule is approximately 1.8 grams.