A uniform metre rule of mass long balance at the 40cm mark when a mass x is placed at the 10cm mark,what is the value of x?
To determine the value of x, we can use the principle of moments or the concept of torque.
The principle of moments states that for an object 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 take moments about the 40cm mark, where the mass balance is balanced when no external force is applied.
Let's assume that the mass balance is balanced. The clockwise moments are produced by the mass of the meter rule, while the anticlockwise moments are produced by the mass, x, at the 10cm mark.
The clockwise moment is given by: (mass of the meter rule) * (distance from the 40cm mark to the center of mass of the meter rule)
The anticlockwise moment is given by: x * (distance from the 10cm mark to the center of mass of the meter rule)
Since the meter rule is uniform, its center of mass is at its midpoint, which is at the 50cm mark. Therefore, the distance from the 40cm mark to the center of mass of the meter rule is 10cm.
Now, let's set up the equation for the principle of moments:
(clockwise moment) = (anticlockwise moment)
(mass of the meter rule) * (10cm) = x * (30cm)
We know the mass of the meter rule is given, so we can substitute the values into the equation:
(mass of the meter rule) * (10cm) = x * (30cm)
Solve the equation for x:
x = (mass of the meter rule) * (10cm) / (30cm)
Plug in the values:
x = (mass of the meter rule) * (1/3)
Therefore, the value of x is one-third of the mass of the meter rule.