# A metre stick is

Let m be the mass of the scale. The centre of mass of scale is at 50 cm. thus scale is balanced at this point.

When 2 coins of mass 5 g are placed at 12 cm, the equilibrium has shifted to 45 cm mark.

Centre of mass of coins are at 12 cm mark and centre of mass of meter stick is at 50 cm mark.

For equilibrium about 45 cm mark,

Wcoin × dcoin = Wmeter stick × dmeter stick

Where

Wcoin is weight of coin which is 10×g

Wmeter scale is weight of meter stick which is mg

dcoin is distance of centre of mass of coin from equilibrium

dmeter scale is distance of centre of mass of meter scale from equilibrium

Thus,

10 g (45 - 12) = m g (50 - 45)

10 g × 33 = mg × 5

m = 10 × 33 /5

m = 66 grams

I.e. The mass of meter stick is 66 grams

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