Consider the diameter of a spherical object being measured with the...

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

\mathrm{x}=0.1 \mathrm{~cm}

when the jaws of Vernier callipers are closed. If the main scale reading for the diameter is

\mathrm{M}=5 \mathrm{~cm}

and the number of coinciding vernier division is 8 , the measured diameter after zero error correction, is

Options

A5.18 cm
B5.08 cm
C4.98 cm
D5.00 cm

Correct answer

C. 4.98 cm

Step-by-step solution

\begin{aligned} & 10 \text{ V.S.D. }=9 \text{ M.S.D. } \\ & 1 \text{ M.S.D. }=0.1 \mathrm{ cm} \text{ (Given) } \\ & 1 \text{ V.S.D. }=0.9 \text{ M.S.D. } \\ & 1 \text{ V.S.D. }=0.9 \times 0.1 \mathrm{ cm} \\ & \therefore \text{ V.S.D. }=0.09 \mathrm{ cm} \\ & \text{ L.C. }=1 \text{ M.S.D. }-1 \text{ V.S.D. } \\ & =(0.1-0.09) \mathrm{cm} \\ & =0.01 \mathrm{ cm} \\ & \text{ Reading }=5.08 \mathrm{ cm} \\ & \text{ Positive zero error }=0.1 \mathrm{ cm} \text{ (Given) } \\ & \therefore \text{ Final Corrected reading }=(5.08-0.1) \mathrm{cm} \\ & =4.98 \mathrm{ cm} \end{aligned}

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