Question

In an experiment with Vernier callipers of least count 0.1 mm, when two jaws are joined together the zero of Vernier scale lies right to the zero of the main scale and 6th division of Vernier scale coincides with the main scale division. While measuring the diameter of a spherical bob, the zero of vernier scale lies in between 3.2 cm and 3.3 cm marks, and 4th division of vernier scale coincides with the main scale division. The diameter of bob is measured as

• A. 3.26 cm
• B. 3.25 cm
• C. 3.22 cm
• D. 3.18 cm

Answer 1

The Correct Option is D

Step 1: Calculating the zero error and the actual measurement. The zero error in the vernier scale is: \[ \text{Zero error} = 6 \times 0.1 \, \text{mm} = 0.6 \, \text{mm} \, (\text{+ve zero error}) \] Now, the diameter measured with the help of the Vernier scale is: \[ \text{Diameter} = \text{Main Scale Reading} + \text{Vernier Scale Reading} \times \text{Least Count} \] \[ \text{Diameter} = 3.2 \, \text{cm} + 0.1 \, \text{mm} \times 4 = 3.2 \, \text{cm} + 0.4 \, \text{mm} = 3.24 \, \text{cm} \] The actual diameter is: \[ \text{Actual diameter} = 3.24 \, \text{cm} - \text{Zero error} = 3.24 \, \text{cm} - 0.06 \, \text{cm} = 3.18 \, \text{cm} \]