Observe the diagram of a uniform metre scale of mass 200 g given below. Weights of 200 gf and 100 gf are suspended from its ends. At which marking will the ruler be balanced?
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Given,
- Weight suspended at the 0 cm mark = 100 gf
- Weight of the uniform metre scale = 200 gf, acting at its centre of gravity i.e., at the 50 cm mark
- Weight suspended at the 100 cm mark = 200 gf
Let the ruler be balanced when the knife edge is placed at the x cm mark.
Taking moments about the knife edge,
Anticlockwise moments (due to the forces to the left of the knife edge)
= 100 x (x - 0) + 200 x (x - 50)
Clockwise moment (due to the force to the right of the knife edge)
= 200 x (100 - x)
By the principle of moments,
Anticlockwise moments = Clockwise moment
$$\begin{aligned}100(\text x - 0) + 200(\text x - 50) = 200(100 - \text x) \\[1em] \Rightarrow 100\text x + 200\text x - 10000 = 20000 - 200\text x \\[1em] \Rightarrow 300\text x - 10000 = 20000 - 200\text x \\[1em] \Rightarrow 300\text x + 200\text x = 20000 + 10000 \\[1em] \Rightarrow 500\text x = 30000 \\[1em] \Rightarrow \text x = \frac{30000}{500} = 60\end{aligned}$$
Hence, the ruler will be balanced at the 60 cm mark.