Length of the narrow bore is given as $L=1 \mathrm{~m}=100 \mathrm{~cm}$
Length of the mercury thread is given as $\mid=76 \mathrm{~cm}$
Length of the air column between mercury and the closed end, $l a=15 \mathrm{~cm}$ air space is:
$=100-(76+15)$
So,
The total length of the air column will be $=15+9=24 \mathrm{~cm}$
Let h cm of mercury flow out as a result of atmospheric pressure
So we have,
Length of the air column in the bore will be $=24+\mathrm{h}$ cm
And,
Temperature remains constant throughout the process
Therefore,
On substituting, we get,
On solving further, we get,
$=23.8 \mathrm{~cm}$ or $-47.8 \mathrm{~cm}$
Since height cannot be negative. Hence, $23.8 \mathrm{~cm}$ of mercury will flow out from the bore
Length of the air column $=24+23.8=47.8 \mathrm{~cm}$