Question

In a physical balance working on the principle of moments, when $5\,mg$ weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct ?

• A. Left arm is longer than the right arm
• B. Both the arms are of same length
• C. Left arm is shorter than the right arm
• D. Every object that is weighed using this balance appears lighter than its actual weight.

Answer 1

Answer: (C)

$
F _{1} d _{1}= F _{2} d _{2}
$
Consider mass of pan be m,as the mass of the pan is same initially, so when the weight is not placed on the pan the force acting will be same as $mg$ on both sides,
$\therefore $ After the weight is placed on left pan,
$
\begin{array}{l}
(5 mg + mg ) d _{1}= mgd _{2} \\
d _{2}=6 d _{1}
\end{array}
$
Hence the left arm(in which $5 mg$ was placed) is shorter than right arm.