Length of the narrow bore is given as

Length of the mercury thread is given as

Length of the air column between mercury and the closed end, air space is:

So,

The total length of the air column will be

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 cm

And,

Temperature remains constant throughout the process

Therefore,

On substituting, we get,

On solving further, we get,

or

Since height cannot be negative. Hence, of mercury will flow out from the bore

Length of the air column