5(b)
A uniform metre scale is in equilibrium as shown in the diagram :
(i) Calculate the weight of the metre scale.
(ii) Which of the following options is correct to keep the ruler in equilibrium when 40 gf wt is shifted to 0 cm mark?
F is shifted towards 0 cm
or
F is shifted towards 100 cm.
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(i) Let W gf be the weight of metre rule which acts downwards from 50 cm mark.
In equilibrium position, taking moments about fulcrum.
Anticlockwise moment = 40 x (30 - 5) = 1000 gf cm
Clockwise moment = W (50 - 30) = 20 W gf cm
∴ Using principle of moments:
20 W = 1000
⇒ W = $\frac{1000}{20}$ = 50 gf
∴ Weight of the metre scale = 50 gf
(ii) In order to keep the ruler in equilibrium, F is shifted towards 0 cm mark.