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A body weighing 8 g when placed in one pan and 18 g when placed on the other pan of a false balance. If the beam is horizontal when both the pans are empty, then the true weight of the body is
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12 g
Consider the diagram in balance
$8 x=w y$
$\Rightarrow \quad \frac{x}{y}=\frac{w}{8}$ ...(i)
Also, $w x=18 y$
$\Rightarrow \quad \frac{x}{y}=\frac{18}{w}$ ...(ii)
Dividing Eq. (i) and Eq. (ii) we get
$\begin{aligned} \frac{x / y}{x / y} & =\frac{\frac{w}{8}}{18 / w} \\ \Rightarrow \quad w & =\sqrt{18 \times 8}=12 \mathrm{~g}\end{aligned}$
$8 x=w y$
$\Rightarrow \quad \frac{x}{y}=\frac{w}{8}$ ...(i)
Also, $w x=18 y$
$\Rightarrow \quad \frac{x}{y}=\frac{18}{w}$ ...(ii)
Dividing Eq. (i) and Eq. (ii) we get
$\begin{aligned} \frac{x / y}{x / y} & =\frac{\frac{w}{8}}{18 / w} \\ \Rightarrow \quad w & =\sqrt{18 \times 8}=12 \mathrm{~g}\end{aligned}$
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