Question

A body weighs $9g$ when placed in one pan of a faulty balance. It weighs $16g$ when placed in the other pan of the same balance. If the beam remains horizontal when the pans are empty, what is the true weight of the body?

• A. $25g$
• B. $12g$
• C. $7g$
• D. $5g$

Answer 1

The correct option is B $12g$

Let ${}^{\prime }{b}^{\prime }$be the actual mass of the body,and $x$ and $y$ be the distance of pan $P_1$ and $P_2$ respectively
Since the pans are faulty and they have their own weights also
Considering torque balance:

Condition-1:
$(P_1+b)\times x=(9+P_2)\times y$

Condition-2:
$(P_1+16)\times x=(P_2+b)\times y$

Also, when pans are empty
$P_{1}x=P_{2}y$
$\therefore bx=9y$
And
$16x=by$
we get
$\frac{b}{16}=\frac{9}{b}$
$\therefore b=12$