Question 157: Units , Dimensions and Error Analysis

Question

One main scale division of a vernier callipers is 'a' cm and nth division of the vernier scale coincide with (n $$-$$ 1)th division of the main scale. The least count of the callipers in mm is :

Accepted Answer

n VSD = (n $$-$$ 1) MSD
1 VSD = $$\left( {{{n - 1} \over n}} \right)$$MSD
L.C. = 1 MSD $$-$$ 1 VSD
= 1 MSD $$-$$ $$\left( {{{n - 1} \over n}} \right)$$MSD
= 1 MSD $$-$$ 1 MSD + $${{MSD} \over n}$$
= $${{MSD} \over n}$$
= $${a \over n}$$ cm
= $${{10a} \over n}$$ mm

Answer

$${{10a} \over n}$$

Answer

$${{10na} \over {(n - 1)}}$$

Answer

$$\left( {{{n - 1} \over {10n}}} \right)a$$

Answer

$${{10a} \over {(n - 1)}}$$

Units , Dimensions and Error Analysis

One main scale division of a vernier callipers is 'a' cm and nth division of the vernier scale coincide with (n $-$ 1)th division of the main scale. The least count of the callipers in mm is :

Choose the correct answer: