A gas column is trapped between the closed end of a tube and an Hg column of length \( h \). When this tube is placed with its end upward, the length of the gas column is \( l_1 \). What is the relationship between \( l_1 \), \( h \), and the original length of the gas column?

a) \( l_1 = h \)

b) \( l_1 > h \)

c) \( l_1 < h \)

d) \( l_1 = 2h \)

The pressure from the Hg column, being denser than the gas, compresses the gas, resulting in a shorter gas column length (l₁) compared to the Hg column length (h). Thus the correct option is c) l₁ < h

Explanation:

When the tube is placed with its closed end upward, the trapped gas experiences two opposing pressures:

Atmospheric pressure (P_atm): Pushing down on the gas column from above.

Mercury pressure (P_Hg): Due to the weight of the Hg column, pushing down from below.

Since the Hg column is denser than the gas, the pressure exerted by the Hg column (P_Hg) is greater than the atmospheric pressure (P_atm). This pressure difference pushes the gas column down the tube, compressing it.

Impact on Gas Column Length:

Original gas column length: Let's denote this as L.

Length of the gas column with the tube upward (l₁): Due to the pressure difference explained above, the gas gets compressed, and its length (l₁) will be shorter than the original length (L).

Therefore, l₁, the length of the gas column when the tube is placed upward, will be less than h, the length of the Hg column. Thus the correct option is c) l₁ < h