Consider the diameter of a spherical object being measured with the help of a Vernier callipers. Suppose its 10 Vernier Scale Div…

Question

Consider the diameter of a spherical object being measured with the help of a Vernier callipers. Suppose its 10 Vernier Scale Divisions (V.S.D.) are equal to its 9 Main Scale Divisions (M.S.D.). The least division in the M.S. is 0.1 cm and the zero of V.S. is at x=0.1 cm when the jaws of Vernier callipers are closed. If the main scale reading for the diameter is M=5 cm and the number of coinciding vernier division is 8, the measured diameter after zero error correction is:

1. A. 5.18 cm
2. B. 5.08 cm
3. C. 4.98 cm (Correct answer)
4. D. 5.00 cm

Correct Answer

Option C — 4.98 cm

Detailed Solution & Explanation

The correct answer is 4.98 cm.

Key Points

• Least count $=1\,\text{MSD}-1\,\text{VSD}=1\,\text{MSD}-\dfrac{9}{10}\,\text{MSD}=\dfrac{1}{10}\times0.1=0.01$ cm.
• Zero error $=+0.1$ cm (zero of vernier at $x=0.1$ cm when jaws closed), so a positive correction of $-0.1$ cm is applied.
• Observed reading $=M+(\text{coinciding div})\times LC=5+8\times0.01=5.08$ cm.
• Corrected diameter $=5.08-0.1=4.98$ cm.