When both jaws of vernier callipers touch each other, zero mark of the vernier scale is right to zero mark of main scale $$4^{th}$$ mark on vernier scale coincides with certain mark on the main scale. while measuring the length of a cylinder, observer observes 15 divisions on main scale and $$5^{th}$$ division of vernier scale coincides with a main scale division. Measured length of cylinder is______mm.
(Least count of Vernier calliper= 0.1 mm)

The reading shown by a vernier calliper has two parts:
  • Main-scale reading (MSR) = value at the mark just left of the vernier zero.
  • Vernier-scale reading (VSR) = (coinciding vernier division) $$\times$$ least count (LC).
Total reading $$=$$ MSR $$+$$ VSR.

Case 1: Determining the zero error (jaws closed)

When the jaws are in contact, the vernier zero is to the right of the main-scale zero; this is a positive zero error.
Here the $$4^{\text{th}}$$ vernier division coincides with a main-scale mark.

MSR = $$0 \text{ mm}$$ because the vernier zero has not crossed the first main-scale division.
VSR $$= 4 \times LC = 4 \times 0.1 \text{ mm} = 0.4 \text{ mm}$$.

Observed zero reading $$= 0 + 0.4 = 0.4 \text{ mm}$$, so
zero error $$= +0.4 \text{ mm}$$ and the zero correction (to be applied later) is $$-0.4 \text{ mm}$$.

Case 2: Measuring the cylinder

The observer notes:
  • MSR = $$15 \text{ mm}$$ (15 main-scale divisions lie to the left of the vernier zero).
  • The $$5^{\text{th}}$$ vernier division coincides with a main-scale mark.

VSR $$= 5 \times 0.1 \text{ mm} = 0.5 \text{ mm}$$.

Raw reading (uncorrected) $$= 15 + 0.5 = 15.5 \text{ mm}$$.

Applying the zero correction
True length $$= 15.5 \text{ mm} - 0.4 \text{ mm} = 15.1 \text{ mm}$$.

Therefore, the measured length of the cylinder is $$\mathbf{15.1 \text{ mm}}$$ (Option B).