In a physical balance working on the principle of moments, when 5   mg weight is placed on the left…

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?
  1. Every object that is weighed using this balance appears lighter than its actual weight
  2. Left arm is shorter than the right arm
  3. Both the arms are of same length
  4. Left arm is longer than the right arm

Solution

Let m 1 and m 2 be the masses of pan

It is given that m1=m2



Since balance is achieved, so net torque about O should be zero.
5 mg+ m 1 g r 1 = m 2 g r 2
⇒5mg+m1gr1=m1gr2
⇒r1r2=m1gm1g+5mg
⇒r1r2<1

So, left arm is shorter than the right arm.

Asked in: JEE Main 2017 (08 Apr Online)

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