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A uniform metre scale is in equilibrium as shown in the diagram :

A uniform metre scale is in equilibrium as shown in the diagram. Calculate the weight of the metre scale. 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. ICSE 2019 Physics Solved Question Paper.

(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.

Force

ICSE 2019

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Answer

(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 = 100020\dfrac{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.

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