(3) 16 cm
Let A be the area of cross–section of the tube. P1 , V1 denote pressure and volume of air in tube intially. P2 , V2 are corresponding quantities when one end of tube has been scaled. Under isothermal conditions
P1V1 = P2V2
or P0 8 x A = P2 x (54-x)A
where x is length of mercury inside tube as shown in Fig.
From Eqns (i) and (ii) we have
The length of air column in closed tube = 54 - 38 = 16 cm