A 10 cm long gas column is trapped by a 4 cm long column of mercury in a capillary tube, as shown below, when the tube is held horizontally in a room at an external pressure of 1 atm. The length of the air column when the tube is held vertically with the open end up is

3.5 cm

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6.2 cm

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9.5 cm

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4.8 cm

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Solution

The correct option is C
9.5 cm

Since temperature is constant; when the tube is horizontal:

$P_{1}$ = 760 mm $V_{1}$ = 10A (A=area of cross section)

When the tube is vertical :

$P_{2}$ = 760 +4 = 764 mm $V_{2}$ = ?

$P_{1} V_{1} = P_{2} V_{2}$

$760 \times 10 A = 764 \times V_{2}$ $V_{2}$ = 9.5A

$∴$ length of air column = 9.5 cm (as area of cross section is the same).

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