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Acceleration Due To Gravity

A mercury bar...

Question

A mercury barometer is known to be defective. It contains a small quantity of air in the space above the mercury. When an accurate barometer reads 770 mm, the defective one reads 760 mm and when the accurate one reads 750 mm, the defective one reads 742 mm. The true atmospheric pressure when the defective barometer reads 750 mm is

A

68 cm of Hg

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B

79.88 cm of Hg

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C

75.88 cm of Hg

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D

72.15 cm of Hg

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Solution

The correct option is B 75.88 cm of Hg
$p r e s s u r e i n e a c h c a s e = a c t u a l p r e s s u r e - o b s e r v e d p r e s s u r e l e n g t h i n e a c h c a s e = a c t u a l l e n g t h - o b s e r v e d l e n g t h A c c o r d i n g t o t h e B o y l e^{'} s l a w 10 \times (l_{0} - 76) = 8 (l_{0} - 74.2) = (P_{0} - 75) (l_{0} - 76) \Rightarrow l_{0} = 83.2 P_{0} = 75.88 c m$

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