. Figure 1.33 shows a uniform metre rule placed on a fulcrum at its mid-point O


Figure 1.33 shows a uniform metre rule placed on a fulcrum at its mid-point O and having a weight 40 gf at the 10 cm mark and a weight of 20 gf at the 90 cm mark. (i) Is the metre rule in equilibrium? If not, how will the rule turn? (ii) How can the rule be brought in equilibrium by using an additional weight of 40 gf?

Metre

 

Best Answer

(i) Anticlockwise moment= 40 gf x (50-10)cm

= 40 gf x 40 cm=1600 gf x cm

Clockwise moment= 20 gf x (90- 50) =20 gf x 40 cm=800 gf x cm

Anticlockwise moment is not equal to clockwise moment. Hence the metre rule is not in equilibrium and it will turn anticlockwise.

(ii)To balance it, 40gf weight should be kept on right hand side so as to produce a clockwise moment about the middle point. Let its distance from the middle be d cm. Then,

clockwise moment= 20 gf x 40 cm + 40 gf x d cm

From the principle of moments,

Anticlockwise moment= Clockwise moment

40 gf x 40 cm= 20 gf x 40 + 40 x d cm

1600-800=40 gf x dcm

So, d= (on the other side)

Hence, by placing the additional weight of 40 gf at the 70 cm mark the rule can be brought in equilibrium.

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