Saturday, December 13, 2008

Q) A body weighs 6 grams when placed on one pan and 24 grams when placed on the other pan of a defective beam balance according to the reading shown on the instrument. If the beam is horizontal when both pans are empty, what is the true weight of the body?

A) Let the left pan have weight m1 and distance l1 from pivot.
Let the right pan have weight m2 and distance l2 from pivot.

Balancing the torques:
m1. l1 = m2.l2 (given that they are balanced when empty)

(X + m1).l1 = (6+m2). l2 -----------------------------(1)

(24 + m1).l1 = (X+m2).l2 ----------------------------(2)

where X is the unknown weight of the body.

Substituting m1.l1 = m2.l2 in both equations above, we get:
l1/l2 = X/24 = 6/X
so X^2 = 24*6

X = 12 gms


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