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Question:

In a physical balance working on the principle of moments, when a 5 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?

Left arm is shorter than the right arm.

Both the arms are of same length.

Every object that is weighed using this balance appears lighter than its actual weight.

Left arm is longer than the right arm.

Solution:

F1d1 = F2d2
Consider mass of pan = m. As the mass of the pan is the same initially, so when the weight is not placed on the pan the force acting will be the same (mg) on both sides.
∴ After the weight is placed on the left pan, (5mg + mg)d1 = mgd2
d2 = 6d1
Hence the left arm (in which 5mg was placed) is shorter than the right arm.