Question

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

Answer 1

Question:-

In a vernier calliper, N divisions of vernier scale coincide with (N-1) divisions of main scale (in which division represent 1mm). Find the least count of the instrument in cm.

Answer:-

$\displaystyle\Large\boxed {\sf {\left (\dfrac {1}{10N}\right)\ cm}}$

Solution:-

• $\displaystyle\sf {M=}$ main scale division (least count of main scale)

• $\displaystyle\sf {V=}$ vernier scale division (least count of vernier scale)

Each main scale division represents 1 mm.

$\displaystyle\longrightarrow\sf{M=\dfrac {1}{10}\ cm}$

N vernier scale divisions coincide with (N - 1) main scale divisions.

$\displaystyle\longrightarrow\sf{NV=(N-1)M}$

$\displaystyle\longrightarrow\sf{V=\left (\dfrac {N-1}{N}\right)M}$

$\displaystyle\longrightarrow\sf{V=\left (\dfrac {N-1}{10N}\right)\ cm}$

Now, least count,

$\displaystyle\longrightarrow\sf{LC=M-V}$

$\displaystyle\longrightarrow\sf{LC=\left (\dfrac {1}{10}-\dfrac {N-1}{10N}\right)\ cm}$

$\displaystyle\longrightarrow\sf{\underline {\underline {LC=\left (\dfrac {1}{10N}\right)\ cm}}}$