Question 133 of 280

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?

AEvery object that is weighed using this balance appears lighter than its actual weightBLeft arm is shorter than the right armCBoth the arms are of same lengthDLeft arm is longer than the right arm

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Answer: (B) Left arm is shorter than the right arm

Let ${m}_{1}$ and ${m}_{2}$ be the masses of pan

It is given that ${m}_{1}={m}_{2}$



Since balance is achieved, so net torque about $O$ should be zero.
$\left(5 mg+{m}_{1}g\right){r}_{1}=\left({m}_{2}g\right){r}_{2}$
$\Rightarrow \left(5mg+{m}_{1}g\right){r}_{1}=\left({m}_{1}g\right){r}_{2}$
$\Rightarrow \dfrac{{r}_{1}}{{r}_{2}}=\dfrac{{m}_{1}g}{{m}_{1}g+5mg}$
$\Rightarrow \dfrac{{r}_{1}}{{r}_{2}}\lt 1$
So, left arm is shorter than the right arm.