In an experiment the angles are required to be measured using an … - Vidyadip

MCQ

In an experiment the angles are required to be measured using an instrument, $29$ divisions of the main scale exactly coincide with the $30$ divisions of the vernier scale. If the smallest division of the main scale is half- a degree $(= 0.5^o )$, then the least count of the instrument is

A
$1^o$
B
$\frac{1}{2}^o$
✓
$1'$
D
$( \frac{1}{2})'$

✓

Answer

Correct option: C.

$1'$

c
$30$ Divisions of vernier scale coincide with $29$
divisions of main scales
Therefore $1\,V.S.D = \frac{{29}}{{30}}MSD$
Least count $= 1\,MSD - 1VSD = 1MSD - \frac{{29}}{{30}}MSD$
$ = \frac{1}{{30}}MSD = \frac{1}{{30}} \times {0.5^ \circ } =$ $1$ minute

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