Question

A body weighs $8g$ when placed in one pan and $18g$ 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:

• A. $13g$
• B. $12g$
• C. $15.5g$
• D. $15g$

Answer 1

Answer: (B)

$12g$

Let the mass of first and second pan be $m_1$ and $m_2$, respectively and their respective distance from the pivot be $L_1$ and $L_2$.

Let the true weight of the body be $M$.

As the beam is horizontal when both the pans are empty, thus net torque about the pivot is zero.

$\therefore$ $m_{1}g{L}_1-m_{2}g{L}_2=0$

We get $m_1{L}_1=m_2{L}_2$ ....(1)

The body weighs $8g$ in first pan.

$\therefore$ $(M+m_1)g{L}_1=(8+m_2)g{L}_2$

Or $M{L}_1=8L_2$ ....(2) (Using (1))

The body weighs $18g$ in second pan.

$\therefore$ $(18+m_1)g{L}_1=(M+m_2)g{L}_2$

Or $18L_1=M{L}_2$ ....(3) (Using (1))

Dividing equation (2) and (3) we get $\frac{M}{18}=\frac{8}{M}$

Or $M^2=8\times 18=144$

$⟹$ $M=12$ g