The atmospheric pressure is measured with a Fortin's barometer having a vernier scale whose $20$ divisions coincide with $19$ divisions of main scale. Each division of the main scale is equal to $0.5 m m$ . Which of the following correctly expresses the atmospheric pressure?

75.0050 c m

of Hg

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75.005 c m

of Hg

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75.00 c m

of Hg

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71.05 c m

of Hg

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Solution

The correct option is A $75.0050 c m$ of Hg
$20$ Vernier scale divisions = $19$ Main Scale divisions (given)

Thus, $1 V S D = \frac{19}{20} M S D$

or Vernier Constant = $1 M S D - 1 V S D$ = $\frac{1}{20} M S D$

Hence, least count of vernier scale = $\frac{1}{20} \times$ $0.5 = 0.025 m m$ or $0.0025 c m$ .
Thus we can get the value as $75.0050$ with this least count, for atmospheric pressure.

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