When a boy is sitting 1 meter from the center of a see-saw, another boy must sit on the opposite side 0.5 meter farther from the center compared to the first boy to maintain balance. When the first boy carries an additional weight of 10 kg and sits 1.5 meters from the center, the second boy must now move to 3 meters from the center to maintain balance. Determine the weight of the two boys.
To solve this problem, we can use the principle of moments. The principle of moments states that for an object in rotational equilibrium, the sum of the clockwise moments about any point must be equal to the sum of the anticlockwise moments about the same point.
Let's denote:
- w1 as the weight of the first boy
- w2 as the weight of the second boy
First, let's analyze the balance without any additional weights. According to the problem:
- The first boy sits 1 meter from the center, so the clockwise moment caused by his weight is 1 * w1.
- The second boy must sit 0.5 meters farther from the center compared to the first boy to maintain balance. So, the second boy sits 1.5 + 0.5 = 2 meters from the center, and the anticlockwise moment caused by his weight is 2 * w2.
Since the see-saw is in balance, the clockwise moment must be equal to the anticlockwise moment:
1 * w1 = 2 * w2 ----(1)
Now, let's consider the situation when the first boy carries an additional weight of 10 kg and sits 1.5 meters from the center. In this case:
- The clockwise moment caused by the weight of the first boy is 1.5 * (w1 + 10) since the distance has increased to 1.5 meters, and the weight is now w1 + 10.
- The second boy must move to 3 meters from the center to maintain balance, so the anticlockwise moment caused by his weight is 3 * w2.
Again, the clockwise moment must be equal to the anticlockwise moment:
1.5 * (w1 + 10) = 3 * w2 ----(2)
Now we have two equations (1 and 2) with two unknowns (w1 and w2). We can solve these equations simultaneously to find the weights of the two boys.
Simplifying equation (1), we get:
w1 = 2w2
Substituting this into equation (2), we have:
1.5 * (2w2 + 10) = 3w2
Expanding and simplifying:
3w2 + 15 = 3w2
Subtracting 3w2 from both sides:
15 = 0
This equation results in an inconsistency, which means there is no solution that satisfies the given conditions. Therefore, the problem might contain an error or inconsistency in the stated conditions.