A uniform metre rule of mass 90g is pivoted at the 40cm mark.if the rule is in equilibrium with an unknown mass m placed at the 10cm mark and a 72 g at the 70cm mark,determine m.?
well, the 10cm and the 70cm marks are at equal distances from the 40cm mark.
So, now the question is, how long is the rule?
To determine the unknown mass (m), we can make use of the principle of moments. According to this principle, the sum of the moments on either side of a pivot point in a balanced system is equal.
In this case, the metre rule is in equilibrium, meaning the total clockwise moment is equal to the total anticlockwise moment.
First, let's find the clockwise moment. The clockwise moment is the product of the mass and the distance from the pivot point.
For the 72g mass at the 70cm mark:
Clockwise moment = 72g x (70cm - 40cm) = 72g x 30cm = 2160g cm²
Next, let's find the anticlockwise moment. We know that the pivot point is at the 40cm mark, so the distance from the pivot to the 10cm mark (where the unknown mass is placed) is 30cm.
For the unknown mass (m) at the 10cm mark:
Anticlockwise moment = m x (40cm - 10cm) = m x 30cm
Since the clockwise and anticlockwise moments must be equal for equilibrium, we can set up an equation:
2160g cm² = m x 30cm
Now, let's solve for m:
m = 2160g cm² / 30cm
m = 72g
Therefore, the unknown mass (m) is 72g.