A body weighing 8 g when placed in one pan and 18 g when placed on...

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

Options

A13 g
B9 g
C22 g
D12 g

Correct answer

D. 12 g

Step-by-step solution

Consider the diagram in balance 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

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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