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Error and Uncertainty

A beam balanc...

Question

A beam balance of unequal arm length is used by an unscruplus trader. When an object is weighed on left pan. The weight $i$ found to be $W_{1}$ . When the object is weighed on the right plan, the weight is found to be $W_{2}$ . If $W_{1} \neq W_{2}$ , the correct weight of the object is

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

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

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\sqrt{W_{1}^{2} {+ W}_{2}^{2}}

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\sqrt{W_{2}^{2} {- W}_{1}^{2}}

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Solution

The correct option is B $\sqrt{W_{1} W_{2}}$

Let the beam balance be as shown.
And let actual weight be $W$ .
(1) $W r_{L} = W_{1} r_{R}$
(2) $W_{2} r_{L} = W r_{R}$
Dividing Equation 1 by Equation 2,
$\frac{W}{W_{2}} = \frac{W_{1}}{W}$
$\Rightarrow W = \sqrt{W_{1} W_{2}}$

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