A uniform half metre rule is balanced horizontally across a knife edge placed 15cm from one end . A mass of 30g is hung from the same end . What is the mass of the metre rule?
30 * 15 = m (50 -15)
Chuck
To solve this problem, we can use the principle of moments. The principle of moments states that for an object to be in equilibrium, the sum of the clockwise moments must be equal to the sum of the anticlockwise moments.
Let's denote the length of the half meter rule as L (L = 50 cm) and the distance from the knife edge to the hanging mass as x (x = 15 cm).
1. Calculate the anticlockwise moment:
The anticlockwise moment is given by the product of the distance from the knife edge to the hanging mass (x) and the mass of the hanging mass (m).
Anticlockwise moment = x * m
2. Calculate the clockwise moment:
The clockwise moment is given by the product of the distance from the knife edge to the other end of the ruler (L - x) and the mass of the ruler (M).
Clockwise moment = (L - x) * M
Since the ruler is balanced horizontally, the anticlockwise and clockwise moments are equal:
x * m = (L - x) * M
3. Substitute the given values:
x = 15 cm = 0.15 m
m = 30 g = 0.03 kg
L = 50 cm = 0.50 m
0.15 * 0.03 = (0.50 - 0.15) * M
0.0045 = 0.35 * M
4. Solve for M:
M = 0.0045 / 0.35
M = 0.0129 kg or 12.9 g
Therefore, the mass of the meter rule is approximately 12.9 grams.
To determine the mass of the meter rule, 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 knife edge as the point of rotation, and we know that the ruler is balanced horizontally.
Let's first calculate the clockwise moment caused by the 30g mass hanging from one end of the ruler.
Clockwise moment = weight of the mass * perpendicular distance from the point of rotation
The perpendicular distance is the distance from the knife edge to the point where the mass is hanging. In this case, it is 15cm (or 0.15m).
Clockwise moment = 0.03 kg * 9.8 m/s^2 * 0.15 m = 0.0441 Nm
Since the ruler is balanced horizontally, the sum of the clockwise moments must be equal to the sum of the anticlockwise moments.
In this case, the only other moment is the mass of the meter rule multiplied by its center of gravity (assuming it is in the center).
So, let's call the mass of the meter rule M.
Anticlockwise moment = mass of the ruler * gravitational acceleration * perpendicular distance
The length of the ruler is 0.5m, and if the ruler is balanced, the distance from the center to the knife edge is 0.25m.
Anticlockwise moment = M kg * 9.8 m/s^2 * 0.25 m = 2.45M Nm
Setting the two moments equal to each other:
0.0441 Nm = 2.45M Nm
Now, solving for M:
M = 0.0441 Nm / 2.45 Nm = 0.018 kg
Therefore, the mass of the meter rule is 0.018 kg or 18 grams.