JEE Main 2017 Physics question

In a physical balance working on the principle of moments, when mg weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?

(1)Every object that is weighed using this balance appears lighter than its actual weight
(2)Left arm is shorter than the right armCorrect
(3)Both the arms are of same length
(4)Left arm is longer than the right arm

Answer: (2)

Solution

With both pans empty and of equal mass , the balance is horizontal only if the moments match: , i.e. only if . Here the beam is **not** horizontal when empty — an extra mg has to be added on the left to level it. That means the right-hand moment was initially

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Question ID VK-115769