A meter rule balance horizontally on a knife edge at the 55cm Mark when a mass of 50g was hung at the 85cm mark. If the balanced point was found to be at the 20cm mark, find (i) the mass of the ruler
(ii) find the distance of the balanced point,if the mass ws moved up to the 70cm mark
To solve this problem, we can use the principle of moments. The principle of moments states that for a balanced system, the sum of the clockwise moments is equal to the sum of the anticlockwise moments.
(i) To find the mass of the ruler, we need to determine the total moment on both sides of the knife edge. Let's call the mass of the ruler M (to be determined).
On the left side of the knife edge (between 0 cm and 20 cm), the moment is given by:
Moment_left = 20 cm × M
On the right side of the knife edge (between 20 cm and 55 cm), we have a mass of 50 g (0.05 kg) at a distance of 30 cm (85 cm - 55 cm):
Moment_right = 30 cm × 0.05 kg = 1.5 kg⋅cm
Since the ruler is balanced, the total moment on both sides must be equal:
20 cm × M = 1.5 kg⋅cm
Solving for M:
M = (1.5 kg⋅cm) / 20 cm
M = 0.075 kg
Therefore, the mass of the ruler is 0.075 kg (or 75 g).
(ii) If we move the mass up to the 70 cm mark, we need to find the new balanced point. Let's call the distance from the knife edge to the new balanced point D (to be determined).
Again, on the left side of the knife edge (between 0 cm and D cm), the moment is given by:
Moment_left = D cm × M
On the right side of the knife edge (between D cm and 70 cm), we now have the 50 g (0.05 kg) mass at a distance of (70 cm - D cm):
Moment_right = (70 cm - D cm) × 0.05 kg
Since the ruler is balanced, the total moment on both sides must be equal:
D cm × M = (70 cm - D cm) × 0.05 kg
Simplifying the equation:
D × 0.075 kg = (70 cm - D cm) × 0.05 kg
0.075D kg = 3.5 kg - 0.05D kg
0.125D kg = 3.5 kg
D = 3.5 kg / 0.125 kg
D = 28 cm
Therefore, when the mass is moved up to the 70 cm mark, the new balanced point will be at the 28 cm mark.
Note: In this solution, we assume that the ruler is of uniform density and the knife edge is frictionless.