An air column, closed at one end and open at the other resonates with a tuning fork when the smallest length of the cloumn is 50 cm. The next larger length of the column resonating with the same tuning frok is:

Explanation

Case 1 : Net pressure on air in volume
` V = (P_atm -h rho g)`
` = 75 xx (rho_Hg) xx g - (10 (rho_Hg)) xx g `
` = rho_Hg xx g xx 65 `
Case 2 : Net pressure on air in volume 'V'.
` = P_atm + (rho_Hg) xx g xx h `
` (P_1)(V_1) = (P_2)(V_2)`
` rArr (rho_Hg) xx g xx 65 xx A xx 20 `
` = ((rho_Hg) xx g xx 75 + (rho_Hg) xx g xx 10) A xx h `
` rArr 65 + 20= 85 h. `
` rArr (h = (65 xx 20 / 85) = 15.2 cm )`
` = 15 cm. `