Question

A uniform metre rule of mass 95g can be balanced horizontally on a knife-edge when a mass of 5g is suspended 10cm from one end. Calculate the distance of the knife-edge from the centre of the rule.​

Answer 1

2 cm

Step-by-step explanation:

The metre rule is 100 cm long. The center of gravity is 50 cm from the end. The 5g mass is 10 cm from the end, so it's 40 cm from the center of the metre rule.

If we say that x is the distance between the knife-edge and the centre of the rule, then summing the moments about the knife-edge:

∑τ = Iα

(5 g) (9.8 m/s²) (40 − x) − (95 g) (9.8 m/s²) (x) = 0

5 (40 − x) = 95 x

200 − 5x = 95x

200 = 100x

x = 2

The distance between the knife edge and the centre of the rule is 2 cm.