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A false balance has equal arms. An object weighs $W_{1}$ when placed in one pan and $W_{2}$ when placed in the other pan. The true weight W of the object is

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$\sqrt{W_{1} W_{2}}$

$\sqrt{{W_{1}}^{2} + {W_{2}}^{2}}$

$\frac{W_{1} + W_{2}}{2}$

$\frac{2 W_{1} W_{2}}{W_{1} + W_{2}}$

answer is C.

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Detailed Solution

Let true weight of the object is W and weight of right pan is x more than left pan.

Now suppose the object is placed in left pan:

W = $W_{1} + x$ ------(1)

Now if the object is placed in right pan.

$W_{2} = W + x$ --------(2)

from (1) and (2) W = $\frac{W_{1} + W_{2}}{2}$

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