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A faulty barometer tube is 90 cm long an...

A faulty barometer tube is 90 cm long and it contains some air above mercury. The reading is 74.5 cm when the true atmospheric pressure is 76 cm. What will be the true atmospheric pressure if the reading on this barometer is 74 cm? (H = 10m of water column)

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Let the area of cross - section of the tube be A `cm^(2)` and true pressure be H cm of mercury. Since the temperature is constant, Boyle.s law can be applied to the air enclosed in the upper part of the barometer tube, thus `P_(1)` = (76.0 - 74.5) = 1.5 cm of mercury
`V_(1)=Axx(90-74.5)=Axx15.5cm^(3)`
`P_(2)=(H-74.0)cm` of mercury
`V_(2)=Axx(90-74.0)=Axx16cm^(3)`
Applying Boyle.s law `P_(1)V_(1)=P_(2)V_(2)`
`1.5xx(Axx15.5)=(H-74)xx(Axx16)`
`H-74=(1.5xx15.5)/16rArrH=74+1.45=75.45cm`
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