Question

Which of the following is the most accurate instrument?

• A. A scale whose least count is 0.1 cm.
• B. A vernier caliper in which 10 vernier divisions coincide with 9 main scale divisions whose main scale is millimetre scale.
• C. A microscope in which 50 vernier divisions coincide with 49 main scale divisions whose main scale is millimetre scale.
• D. A microscope in which 50 vernier divisions coincide with 49 main scale divisions and in the main scale there are 20 divisions in 1 cm.

Answer 1

The correct option is D A microscope in which 50 vernier divisions coincide with 49 main scale divisions and in the main scale there are 20 divisions in 1 cm.

In choice (A), Least count is $0.1cm$
In choice (B), $10v.s.d.=9m.s.d$

L.C. $=1m.s.d.-1v.s.d$
$=\frac{1}{10}\times 0.1=0.01cm$
$=\frac{1}{10}m.s.d$

In choice (C), L.C. $=\{1-\frac{49}{50}\}m.s.d$
$=\frac{1}{50}m.s.d$
$=\frac{1}{50}\times 0.1$
$=0.002$ $cm$

In choice (D), L.C. $=\{1-\frac{49}{50}\}m.s.d$
$=\frac{1}{50}m.s.d$
$=\frac{1}{50}\times 0.05$
$=0.001$ $cm$
$\Rightarrow$ Instrument (D) is most accurate.