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  4. The smallest division on the main scale of a vernier calipers is 1mm, and 10 vernier divisions coincide with 9 main scale divisions. While measuring the diameter of a sphere, the zero mark of the vernier scale lies between 2.0 and 2.1cm and the fifth division of the vernier scale coincides with a scale division. The diameter of the sphere is:

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Q. The smallest division on the main scale of a vernier calipers is $1mm,$ and $10$ vernier divisions coincide with $9$ main scale divisions. While measuring the diameter of a sphere, the zero mark of the vernier scale lies between $2.0$ and $2.1cm$ and the fifth division of the vernier scale coincides with a scale division. The diameter of the sphere is:

NTA AbhyasNTA Abhyas 2022

Solution:

The main scale reading of vernier calipers is $MSR=2cm$ . The least count of the vernier calipers is given by,
$LC=\frac{10 - 9}{100}=0.01cm$
Then the diameter of the sphere is given by,
$D=MSR+n\times \left(L C\right)$ ; where $n$ is the division at which vernier scale coincides with the main scale.
$D=2\times 1+5\times 0.01=2.05cm$ .