A uniform meter strick is found to balance at 50cm mark when placed on fulcrum. When 50g mass is attached at the 102457cm mark, the fulcrum must be moved to the 40cm mark for balance. what is the mass of the meter strick?
To solve this problem, we can use the principle of moments.
The principle of moments states that for an object in equilibrium, the sum of the clockwise moments about any point is equal to the sum of the anticlockwise moments about the same point.
In this case, we can consider the fulcrum point as the point where the moments are balanced.
Given that the meter stick balances at the 50 cm mark without any additional weight, we can assume that the center of mass of the meter stick is at the 50 cm mark.
Let's calculate the moments on both sides of the fulcrum when the 50 g mass is placed at the 102.457 cm mark.
On the left side of the fulcrum (50 cm mark):
The weight of the meter stick acts vertically downward at the center of mass (50 cm mark), so the moment arm is 50 cm.
The moment on the left side is 0 (since the meter stick balances), so we don't need to consider this.
On the right side of the fulcrum (102.457 cm mark):
The weight of the 50 g mass acts vertically downward at the 102.457 cm mark, so the moment arm is 102.457 - 50 = 52.457 cm.
The moment on the right side is 50 g x 52.457 cm.
Since the fulcrum needs to be moved to the 40 cm mark to balance the moments, we need to consider the moments on both sides of the fulcrum.
On the left side of the fulcrum (40 cm mark):
The weight of the meter stick acts vertically downward at the 50 cm mark, so the moment arm is 50 - 40 = 10 cm.
The moment on the left side is mass of the meter stick x 10 cm.
On the right side of the fulcrum (102.457 cm mark):
The weight of the 50 g mass acts vertically downward at the 102.457 cm mark, so the moment arm is 102.457 - 40 = 62.457 cm.
The moment on the right side is 50 g x 62.457 cm.
Since the moments on both sides of the fulcrum need to balance, we can equate the moments:
mass of the meter stick x 10 cm = 50 g x 62.457 cm
To find the mass of the meter stick, we can rearrange the equation:
mass of the meter stick = (50 g x 62.457 cm) / 10 cm
mass of the meter stick = 312.285 g
Therefore, the mass of the meter stick is approximately 312.285 g.