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Question
A faulty balance of unequal arms and pans of unequal weights is used to find the true weight of a metal. By double weighing the weights are found to be 1210 g and 1000 g. Calculate the true weight of the metal.
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Solution
(mL + 1210) x = (mR + mo) y ..............(1)
(mL + m0) x = (mR + 1000) y .............(2)
mL x = mR y ..............(3)
Equations when the two pans are empty from (1)
mL x + 1210 x = mR y + mo y
⇒ 1210 x = mo y ...............(4) (using 3)
from (2)
mL + mo x = mR + 1000 y
⇒ mo x = 1000 y ................(5) (using 3)
dividing equation (4) & (5)
`"m"_"o"/1000 = 1210/"m"_"o"`
⇒ mO = `sqrt (1210 xx1000)` = 1100 g
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