Question

Least count of a vernier calliper is 0.01 cm. When the two jaws of the instrument touch each other the 5th division of the vernier scale coincides with a main scale division and the zero of the vernier scale lies to the left of the zero of the main scale. Furthermore while measuring the diameter of a sphere, the zero mark of the vernier scale lies between 2.4 cm and 2.5 cm and the 6th Vernier division coincides with a main scale division. Calculate the diameter of the sphere.

• A. $2.51cm$
• B. $5.12cm$
• C. $2.51mm$
• D. $5.12mm$

Answer 1

The correct option is A

$2.51cm$

Step 1. Given data:

Least count = $0.01cm$

Main scale reading (MSR) = $2.4cm$

Vernier scale divisions (VSD) = $6$

Step 2. Calculations:

The instrument has a negative error.

$$\begin{gathered} e=\left(-5\times 0.01\right) \\ e=-0.05cm \end{gathered}$$

So the combined reading of the diameter of the sphere

$$\begin{gathered} R=MSR+(VSD\times LC)+Zeroerror \\ R=2.4+\left(6\times 0.01\right)+\left(0.05\right) \\ R=2.51cm \end{gathered}$$

The diameter of the sphere is 2.51 cm.

Hence, the correct option is option A.