To find the position where a mass of 50g should be placed in order for the meter stick to balance horizontally, we can use the principle of moments.
The principle of moments states that for an object to be in rotational equilibrium, the sum of the clockwise moments must be equal to the sum of the counterclockwise moments.
In this case, let's consider the counterclockwise moments as positive and the clockwise moments as negative.
Since the meter stick is balanced at the 30 cm mark, the distance from the pivot (30 cm mark) to the fulcrum is zero. Therefore, we can ignore it in our calculations.
Now, let's calculate the moments caused by each mass:
1. The moment caused by the 100g mass at the 30 cm mark is 0, as its distance from the fulcrum is zero.
2. The moment caused by the 200g mass at the 10 cm mark can be calculated as:
Moment = mass × distance from fulcrum
Moment = 200g × 10cm
3. The moment caused by the 50g mass at an unknown position can be calculated as:
Moment = 50g × distance from fulcrum
Since the meter stick is in rotational equilibrium, the sum of the moments must be zero:
0 + (200g × 10cm) + (50g × distance from fulcrum) = 0
Now, we can solve for the distance from the fulcrum where the 50g mass should be placed:
(200g × 10cm) + (50g × distance from fulcrum) = 0
(200g × 10cm) = -(50g × distance from fulcrum)
2000g cm = -50g × distance from fulcrum
distance from fulcrum = (2000g cm) / -50g
distance from fulcrum = -40 cm
Therefore, a mass of 50g should be placed at the 40 cm mark in order for the meter stick to balance horizontally.