A barometer is an instrument that is used for the measurement of pressure The construction of the barometer is as follows:

A thin narrow calibrated capillary tube is filled to the brim with a liquid such as mercury and is inverted into a through filled with the same fluid Now depending on the external atmospheric pressure the level of the inside capillary comes to rest, then the net forces on the column should be balanced Applying force balance we get `P_(atm)xxA=mxxg`
(A is the cross-sectional area of the capillary tube) if `rho` is the density of the fluid, then `m=rhoxxgxxh`
(h is the height to which mercury has risen in the capillary)
Hence `P_(atm)xxA=(rhoxxgxxh)xxA or P_(atm)=rhogh`
Faulty Barometer:
An ideal barometer will show a correct reading only if the space above the mercury column is vacuum but in case if some gas column is trapped in the space above the mercury column then the barometer is classified as a faulty barometer. The reading of such a barometer will be less than the true pressure

For such a faulty barometer
`P_(0)A=mg+P_(gas)A`
`P_(0)=rhohg+P_(gas)`
or `rhogh=P_(0)-P_(gas)`
A gas column is trapped between closed end of a tube and a mercury column of length (h) when this tube is placed with its open end upwards the length (h)when this tube is placed with its open end upwards the length of gas column is `(l_(1))` the length of gas column becomes `(l_(2))` when open end of tube is held downwards (as shown in figure) find atmospheric in terms of height of Hg column. (Assume temeperature remains constant)

Options

A. `(h(l_(1)+l_(2)))/(l_(2)-l_(1)`
B. `(h(l_(2)+l_(1)))/(l_(1)-l_(2)`
C. `(l_(1)+l_(2))/(h(l_(2)-l_(1))`
D. `(h_(1)l_(1)+h_(2)l_(2))`

Answer

a