1. Tardigrade
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  4. 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 :

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Q. 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 :

Laws of Motion

Solution:

Let length of beam is ' $l$ ', and the two pans are at a distance of ' $x$ ' and ' $l-x$ ' from the hinged point. If true weight of body is $A$, then
$A x =6(l-x) \,\,\,$...(1)
$A(1-x) =24 x\,\,\,$ ...(2)
2Dividing (1) by (2), we get
$\frac{6}{A} =\frac{A}{24} $
$A^{2} =144 $
$A =12 \,g m$