To solve this problem, we need to use the principle of moments (or torque), which states that for a seesaw to be balanced, the moments (torque) around the fulcrum should be equal. Mathematically, this can be expressed as:
[tex]\[ \text{moment of Keshav} = \text{moment of Arjun} \][/tex]
The moment (torque) is the product of the force (weight) and the distance from the fulcrum. For Keshav:
[tex]\[ \text{moment of Keshav} = \text{keshav's weight} \times \text{keshav's distance from the fulcrum} \][/tex]
Given:
- Keshav's weight = 600 N
- Keshav's distance from the fulcrum = 2 m
So, the moment of Keshav is:
[tex]\[ 600 \, \text{N} \times 2 \, \text{m} = 1200 \, \text{Nm} \][/tex]
For the seesaw to be balanced, the moment of Arjun needs to be equal to the moment of Keshav. Therefore:
[tex]\[ \text{moment of Arjun} = 1200 \, \text{Nm} \][/tex]
Arjun's moment can also be written in terms of his weight and distance from the fulcrum:
[tex]\[ \text{moment of Arjun} = \text{arjun's weight} \times \text{arjun's distance from the fulcrum} \][/tex]
Given:
- Arjun's weight = 300 N
We need to find Arjun's distance from the fulcrum, let's call this distance [tex]\( d \)[/tex]. So:
[tex]\[ 300 \, \text{N} \times d = 1200 \, \text{Nm} \][/tex]
To solve for [tex]\( d \)[/tex]:
[tex]\[ d = \frac{1200 \, \text{Nm}}{300 \, \text{N}} \][/tex]
[tex]\[ d = 4 \, \text{m} \][/tex]
Therefore, Arjun should sit 4 meters from the fulcrum to balance Keshav.
