A body weighs 6 gms when placed in one pan and 24 gms when placed on other pan of a false balance. I

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6.System of Particles and Rotational Motion

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$A$ body weighs $6$ gms when placed in one pan and $24$ gms when placed on the other pan of a false balance. If the beam is horizontal when both the pans are empty, the true weight of the body is ....... $gm$.

A

$13$

B

$12$

C

$15.5$

D

$15$

Solution

Let the true weight of body be $w.$

case $1$

When body is placed in left pan

since the balance is in equilibrium,

$8 p=w q$

$\Rightarrow \frac{p}{q}=\frac{w}{8}$ $…(i)$

Case $2:$

When the body is placed in right pan

$\mathrm{w} p=18 q$

$\Rightarrow \frac{p}{q}=\frac{18}{w}$ $…(ii)$

From Eqs. $(i)$ and $(ii),$ we get

$\frac{p}{q}=\frac{w}{8}=\frac{18}{w}$

$w=\sqrt{18 \times 8}=12 g$

Standard 11

Physics

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