To measure the diameter of a spherical object with Vernier calipers, consider the following details:

Vernier Scale and Main Scale Relationship: 10 Vernier Scale Divisions (V.S.D.) are equivalent to 9 Main Scale Divisions (M.S.D.).

Least Value on Main Scale: 0.1 cm

Zero Error: The zero marking on the Vernier Scale (V.S.) is at 0.1 cm when the caliper jaws are closed.

Given measurements:

Main Scale Reading: $ M = 5 \, \text{cm} $

Coinciding Vernier Division: 8

Calculations:

Determining the Least Count:

$ \text{Least Count} = \text{1 MSD} - \text{1 VSD} $

$ = 1 \times 0.1 \, \text{cm} - \frac{9}{10} \times 0.1 \, \text{cm} $

$ = 0.1 \, \text{cm} - 0.09 \, \text{cm} = 0.01 \, \text{cm} $

Accounting for Zero Error:

Zero Error = +0.1 cm

Vernier Scale Reading Calculation:

$ = 8 \times 0.01 \, \text{cm} = 0.08 \, \text{cm} $

Final Diameter Measurement After Zero Error Correction:

$ \text{Measured Diameter} = \text{Main Scale Reading} + \text{Vernier Reading} - \text{Zero Error} $

$ = 5 \, \text{cm} + 0.08 \, \text{cm} - 0.1 \, \text{cm} $

$ = 4.98 \, \text{cm} $

Thus, the corrected measurement for the diameter is 4.98 cm.