Akash takes a uniform metre scale and suspends a weight of 2 N at one end ‘X’, and a weight of 5 N on the other end ‘Y”. He then balances the ruler horizontally…

The diagram of the arrangement is shown below :

Given,

Weight at the end X (W₁) = 2 N

Weight at the end Y (W₂) = 5 N

Distance of X from the knife (R₁) = 70 cm

Distance of Y from the knife (R₂) = 100 cm - 70 cm = 30 cm

Let,

W = weight of the scale

Now,

Anticlockwise moment (due to 2N) = R₁ x W₁ = 2 × 70 = 140 Nm

Clockwise moment (due to 5N) = R₂ x W₂ = 5 × 30 = 150 Nm

Anticlockwise moment (due to weight of the scale) = W × 20 = 20 W

For equilibrium,

Anticlockwise moment of force about knife = Clockwise moment of force about knife

$$\begin{aligned}150 = 140 + 20\text { W} \\[1em] 20 \text W = 150 - 140 = 10 \\[1em] \text W = \frac{10}{20} = 0.5\ \text N\end{aligned}$$

So, weight of the scale is 0.5 N.