A uniform metre rule is pivoted at the 40cm mark. If the metre rule is cut into two equal halves along the midpoint , which half will weigh more?
Please provide an answer with a suitable explanation and diagram if possible.
Note; the answer is not that the two halves weigh the same
Please provide an answer with a suitable explanation and diagram if possible.
Note; the answer is not that the two halves weigh the same
Answers & Comments
Answer:
The half of the meter rule that is closer to the 0cm end of the rule will weigh more.
Explanation:
When the uniform meter rule is pivoted at the 40cm mark and cut into two equal halves at the midpoint, the half that is closer to the 0cm end of the rule will weigh more.
To see why, let's consider the torques on either side of the pivot point. The torque on each side of the pivot point is equal to the weight of that half of the meter rule multiplied by its distance from the pivot point.
Since the two halves of the meter rule have the same mass per unit length, their masses are proportional to their lengths. Therefore, the half of the meter rule that is closer to the 0cm end of the rule will have more mass and will weigh more.
Thus, the half of the meter rule that is closer to the 0cm end of the rule will exert a greater torque on the pivot point, causing it to be the heavier half.
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