Question

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

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

Answer 1

The correct option is D Left arm is shorter than the right arm.

$F_1{d}_1=F_2{d}_2$

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,

$(5mg+mg)d_1=mg{d}_2$

$d_2=6d_1$

Hence the left arm(in which $5mg$ was placed) is shorter than right arm.