Question

In a vernier callipers, one main scale division is x cm and n divisions of the vernier scale coincide with (n-1) divisions of the main scale. The least count (in cm) of the callipers is :-

Answer 1

Question:-

In a vernier callipers, one main scale division is x cm and n divisions of the vernier scale coincide with (n-1) divisions of the main scale. Find the least count (in cm) of the callipers.

Answer:-

$\displaystyle\Large\boxed {\sf {\left (\dfrac {x}{n}\right)\ cm}}$

Solution:-

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

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

One main scale division is x cm.

$\displaystyle\longrightarrow\sf{M=x\ cm}$

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

$\displaystyle\longrightarrow\sf{nV=(n-1)M}$

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

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

Now, least count,

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

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

$\displaystyle\longrightarrow\sf{\underline {\underline {LC=\left (\dfrac {x}{n}\right)\ cm}}}$