1. Principle of a physical balance

A balance works on the principle of moments. If the beam is horizontal, then the clockwise and anticlockwise moments about the fulcrum must be equal.

Let:

• left arm length $= l_L$
• right arm length $= l_R$
• mass of each empty pan $= m$

Since both empty pans have equal mass, their weights are equal.

2. Condition given in the question

When an additional $5\,\text{mg}$ mass is placed on the left pan, the beam becomes horizontal.

This means that before placing the 5 mg weight, the balance was not horizontal, and the right side had greater moment than the left side.

Why?

• The two pans have equal masses.
• So any imbalance must be due to unequal arm lengths.
• Since adding extra weight to the left pan restores balance, the left side originally had smaller moment.

3. Moment equation after placing 5 mg on left pan

When balanced,

Cancelling $g$,

So,

Since $\dfrac{m+5\,\text{mg}}{m} > 1$,

Thus, the right arm is longer, or equivalently,

4. Checking the options

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

(An unequal-arm balance does not necessarily make every object appear lighter; the error depends on how weighing is performed.)

5. Final answer

The correct option is

This matches the stored correct answer.