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  4. In a vernier calliper, N divisions of vernier scale coincide with (.N-1.) divisions of main scale (in which 1 division represents 1mm ). The least count of the instrument in cm . should be

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Q. In a vernier calliper, $N$ divisions of vernier scale coincide with $\left(\right.N-1\left.\right)$ divisions of main scale (in which $1$ division represents $1mm$ ). The least count of the instrument in $cm$ . should be

NTA AbhyasNTA Abhyas 2020

Solution:

$L.C=M.S.D-V.S.N$
Given $\left(\right.N-1\left.\right)M.S.D=N\left(\right.V.S.D\left.\right)$
V.S.D = $\frac{\left(\right. N - 1 \left.\right)}{N}M.S.D$
$L.C=M.S.D$ - $\frac{\left(\right. N - 1 \left.\right)}{N}M.S.D$
$=M.S.D\left(\frac{1}{ N}\right)$