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  4. A body weights 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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Q. A body weights $8 \, g$ 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

NTA AbhyasNTA Abhyas 2022

Solution:

From figure
Solution
$8p=wq$
$\Rightarrow \, \, \frac{p}{q}=\frac{w}{8}$ .... (i)
Now, from figure,
Solution
$wp=18q$
$\Rightarrow \, \, \frac{p}{q}=\frac{18}{w}$ ..... (ii)
From equations (i) and (ii), we get
$\frac{p}{q}=\frac{w}{8}=\frac{18}{w}$
$w=\sqrt{18 \times 8}=12 \, g$