A uniform metre scale of mass 60g, carries masses of 20g, 30g and 80g from points 10cm, 20cm and 90cm marks. Where must the knife edge be placed to balance the scale?
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Answer:
The knife edge must be placed at a distance of 71.05 cm from the 0 cm mark to balance the scale.
Explanation:
Let's assume that the knife edge is placed at a distance x from the 0 cm mark. We can then use the principle of moments to find the position of the knife edge.
The principle of moments states that the sum of the clockwise moments about a point is equal to the sum of the anticlockwise moments about the same point. In this case, we can take the point to be the knife edge, and consider the moments due to the masses and the weight of the scale.
Clockwise moments:
The 20g mass has a moment of 20g x (x - 10cm)
The 30g mass has a moment of 30g x (x - 20cm)
The 80g mass has a moment of 80g x (x - 90cm)
The scale has a moment of 60g x (x - 50cm), where 50cm is the midpoint of the scale.
Anticlockwise moments:
The weight of the scale has a moment of 60g x (50cm - x), where 50cm is the midpoint of the scale.
Setting the sum of the clockwise moments equal to the sum of the anticlockwise moments, we get:
20g x (x - 10cm) + 30g x (x - 20cm) + 80g x (x - 90cm) + 60g x (x - 50cm) = 60g x (50cm - x)
Simplifying and solving for x, we get:
20x - 200 + 30x - 600 + 80x - 7200 + 60x - 3000 = 3000 - 60x
190x = 13500
x = 71.05 cm (rounded to two decimal places)
Therefore, the knife edge must be placed at a distance of 71.05 cm from the 0 cm mark to balance the scale.
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