A meter rule is found to balance at the 32cm mark. When a body of mass 48g is suspended at the 9cm mark, the balance point is found to be 25cm mark. Find
A. The mass of the ruler
B. The distance of the balance point from the zero end of the body were moved to 10cm mark.
To solve this problem, we will use the principle of moments. The principle of moments states that for an object to be in equilibrium, the sum of the anticlockwise moments about any point must be equal to the sum of the clockwise moments about the same point.
Let's denote the mass of the ruler as M and the distance of the balance point from the zero end as x.
A. Finding the mass of the ruler (M):
Given that the balance point is at the 32cm mark, we can assume that the center of mass of the ruler is at this point. Since the ruler is balanced, the sum of the anticlockwise moments must be equal to the sum of the clockwise moments.
Considering the balance point at 32cm and the 48g mass at the 9cm mark, we have:
Sum of anticlockwise moments = Sum of clockwise moments
M * (32cm - x) = 48g * (9cm)
Converting grams to kilograms:
48g = 0.048kg
32cm - x = 0.048kg * 9cm / M
32cm - x = 0.432kg/cm
B. Finding the new distance of the balance point (x) when the body is moved to the 10cm mark:
Given that the new position is at the 25cm mark, we can update the equation:
M * (25cm - x) = 48g * (10cm)
Converting grams to kilograms:
48g = 0.048kg
25cm - x = 0.048kg * 10cm / M
25cm - x = 0.48kg/cm
Now, we have a system of two equations:
1) 32cm - x = 0.432kg/cm
2) 25cm - x = 0.48kg/cm
We can solve this system of equations to find the values of M (mass of the ruler) and x (distance of the balance point).
Once we find the values of M and x, we can substitute them back into the equations to get the final answers:
A. The mass of the ruler (M)
B. The distance of the balance point from the zero end when the body is moved to the 10cm mark (x)