QQuestion
A metre scale of weight 50 gf can be balanced at 40 cm mark without any weight suspended on it.
(a) If this ruler is cut at its centre then state which part [0 to 50 cm or 50 to 100 cm] of the ruler will weigh more than 25 gf.
(b) What minimum weight placed on this metre ruler can balance this ruler when it is pivoted at its centre?
✓Answer
(a) Let the weights of the portions on the two sides of the 40 cm mark be W1 and W2.
W1 + W2 = 50 gf
Taking moments about the 40 cm mark:
40W1 = 60W2
40(50 − W2) = 60W2
W2 = 20 gf and W1 = 30 gf
Therefore, the 0 to 50 cm part of the ruler will weigh more than 25 gf.
(b) The weight of the scale acts at the 40 cm mark. For the minimum weight m placed at the 100 cm mark:
50(50 − 40) = m(100 − 50)
m = 10 gf
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