Question 117: Units , Dimensions and Error Analysis

Question

If n main scale divisions coincide with (n + 1) vernier scale divisions. The least count of vernier callipers, when each centimetre on the main scale is divided into five equal parts, will be :

Accepted Answer

5 parts of main scale division = 1 cm
$$	herefore$$ 1 part of main scale division = $${1 \over 5}$$ cm
$$	herefore$$ 1 M.S.D. = $${1 \over 5}$$ cm
(n + 1) vernier scale division = n main scale division.
$$	herefore$$ 1 V.S.D. = $${n \over n+1}$$ M.S.D.
= $${n \over n+1}$$ $$	imes$$ 1 M.S.D.
= $${n \over n + 1}$$ $$	imes$$ $${1 \over 5}$$ cm
We know,
L.C. = 1 M.S.D. $$-$$ 1 V,S.D.
= $${1 \over 5}$$ cm $$-$$ $${n \over {5(n + 1)}}$$ cm
= $${{n + 1 - n} \over {5(n + 1)}}$$ cm
= $${1 \over {5(n + 1)}}$$ cm

Answer

$${2 \over {n + 1}}$$ mm

Answer

$${5 \over {n + 1}}$$ mm

Answer

$${1 \over {2n}}$$ mm

Answer

$${1 \over {5n}}$$ mm

Units , Dimensions and Error Analysis

If n main scale divisions coincide with (n + 1) vernier scale divisions. The least count of vernier callipers, when each centimetre on the main scale is divided into five equal parts, will be :

Choose the correct answer: