A uniform metre rule is found to balance at the 48cm mark. When a body of mass 60g is suspended at the 6cm mark the balance point is at the 30cm mark. Calculate
a. The mass of the metre rule
b. The distance of the balance point from the zero end if the body were moved to 13cm
Yes
To solve this problem, we need to understand the principles of moments and equilibrium. The principle of moments states that for an object to be in equilibrium, the sum of the clockwise moments (moments that tend to rotate the object clockwise) must be equal to the sum of the anticlockwise moments (moments that tend to rotate the object anticlockwise).
Given information:
- Balance point without any mass: 48 cm
- Balance point with a mass of 60 g at the 6 cm mark: 30 cm
a. Finding the mass of the meter rule:
Let's assume the mass of the meter rule is M grams.
1. The moment on the left side (anticlockwise moment) can be calculated as M * (48 cm - 0 cm) = 48M.
2. The moment on the right side (clockwise moment) can be calculated as 60 g * (30 cm - 6 cm) = 60 * 24 = 1440 (Note: mass is given in grams and distances are in centimeters).
3. Since the meter rule is balanced, the anticlockwise moment is equal to the clockwise moment:
48M = 1440.
4. Solving for M: M = 1440 / 48 = 30 g.
Therefore, the mass of the meter rule is 30 grams.
b. Finding the distance of the balance point from the zero end if the body were moved to 13 cm:
Let's assume the new balance point is at x cm from the zero end.
1. The moment on the left side (anticlockwise moment) can be calculated as M * (48 cm - x cm) = (48 - x)M.
2. The moment on the right side (clockwise moment) remains the same, which is 60 g * (30 cm - 6 cm) = 1440.
3. Since the meter rule is balanced, the anticlockwise moment is equal to the clockwise moment:
(48 - x)M = 1440.
4. Substituting the value of M we found earlier (30 g):
(48 - x) * 30 = 1440.
5. Solving for x:
1440 / 30 = 48 - x.
48 - x = 48.
-x = 48 - 48.
-x = 0.
x = 0.
Therefore, the balance point from the zero end if the body were moved to 13 cm would still be at the zero end.