Question

A uniform metre rule balanes on a knife edge placed at the 60cm mark whem a weight of 2N is suspended from one end calculate the weight of the metre rule

Answer 1

The ruler weights m kilograms.

(there is nothing interesting on the 60-cm end, that is why it is not shown)

Since the ruler is uniform, we can say that the centre of mass of the 60-cm long side is at the centre, or the lever 30 cm. The 60-cm long part weights

$$P_{60}=mg\frac{60}{100}.$$

The centre of mass of the 40-cm end is at the centre as well, the lever for this is 20 cm. The weight is

$$P_{40}=mg\frac{40}{100}.$$

On the 40-cm end, there is 2 N attached at the 100-cm mark. The lever for 2 N is 40 cm. The system is in equilibrium, which means

$$\sum d_{i\text{ left}}P_{i\text{ left}}=\sum d_{i\text{ right}}P_{i\text{ right}}\\ 30P_{60}=20P_{40}+40\cdot P_\text{2N},\\ 30\cdot mg\frac{60}{100}=20\cdot mg\frac{40}{100}+40\cdot2,\\ m=0.82\text{ kg}.$$