Question

In an instrument, there are 25 divisions on the vernier scale which coincides with 24th division of the main scale. 1 cm on main scale is divided into 20 equal parts. The least count of the instrument is

• A. $0.002\text{cm}$
• B. $0.05\text{cm}$
• C. $0.001\text{cm}$
• D. $0.02\text{cm}$

Answer 1

The correct option is A $0.002\text{cm}$

Its given that,
$24M.S.D.=25V.S.D.$
$\Rightarrow 1V.S.D.=\frac{24}{25}M.S.D.$

Least count is given by:
$L.C.=1M.S.D.-1V.S.D.$
$L.C.=1M.S.D.-\frac{24}{25}M.S.D.$
$L.C.=\frac{1}{25}M.S.D.$

As given, $1M.S.D.=1/20cm$
$L.C.=\frac{1}{25}\times \frac{1}{20}cm=0.002cm$