An ideal gas is trapped between a mercury column and the closed lower end of a narrow vertical tube of uniform bore. The upper end of the tube is open to atmosphere (atmospheric pressure = 76 cm of Hg). The length of mercury and the trapped gas columns are 20 cm and 43 cm respectively. What will be the length of the gas column when the tube is titled slowly at constant temperature in a vertical plane through an angle of `60^(@)` ?

Explanation

Case 1 : Atmospheric pressure + Pressure
due to mercury column
Case 2 : Atmospheric pressure +
Component of the pressure due
to mercury column
`((P_1)(V_1) = (P_2)(V_2))`
` rArr (76 xx (rho_Hg) xx g + (rho_(Hg)) xx g xx 20 ) xx A xx 43`
` = (76 xx(rho_(Hg)) xx g + (rho_ (Hg)) xx g`
` xx 20 xx (cos 60 ^@) xx A xx 1 `
` rArr 96 xx 43 = 86 xx L `
` rArr L= (96 xx 43 / 86 ) = 48 cm. `