Question

Fig. 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 ?

Answer 1

(i) Anticlockwise moment = 40 × (50 – 10)

= 1600 gf cm

Clockwise moment = 20 × (90 – 50)

= 800 gf cm.

Since anticlockwise moment is greater than the clockwise moment, so it is not in equilibrium.

(ii) For equilibrium suspend the 40gf at a distance x to the right of 50 cm mark.

Then, 1600 = 800 + 40x

⇒ 40x = 800

x=20 cm

The 40 g has to be suspended at (50 + 20) = 70 cm