A 10 cm column of air is trapped by a column of mercury, 8 cm long, in a capillary tube  horizontally fixed as shown below, at 1 atm pressure. When the tube is held at  certain angle `theta^@` with open end up, the weight of Hg is borne partially by the gas. Vertical Height of Hg is a measure of additional pressure on gas.

When the tube's held at `45^@ `with the horizontal with open end up the length of air column is

Options

A. `(76 xx 10)/(76 + 8/(sqrt2)) cm`
B. `(76 xx 8/(sqrt2))/(76 + 10) cm`
C. `76 xx 8/(sqrt2)`
D. `10 xx 8/(sqrt2)`

Answer

A

Explanation

At `45^@C`, pressure on gas = `76 + h cos theta`
`= 76 + 8/(sqrt(2))`
`P_1l_1 = P_2l_2 , 76 xx 10 = (76 + 8/(sqrt2))l_2`.