Two liquids of densities `2 rho " and " rho` having their volumes in the ratio `3 : 2` are mixed together. Density of the mixture will be

Answer

5

Explanation

` V_2 = V- V_1 = k ( h ^ 3 - d ^ 3 ) `, k = constant , ` V_ 1 ` = volume of the cone in top liquid
`V_2 ` = volume o of the cone in bottom liquid , ` V = kh ^ 3 ` = total volume of the cone For equilibrium, ` rho _s = (V_1 + V_2 ) = rho V_1 + 2 rho V_2 ) `
` rho rho _ sh ^ 3 = rho d ^3 + 2rho (h ^ 3 - d ^ 3 ) rArr rho _s h^3 = 2 rho h^3 - rho d ^ 3 rArr rho d ^3 = h ^ 3 (2 rho - rho _ s ) `
` rArr d ^ 3 = h ^ 3 ( 2 - (rho _s )/(rho )) rArr d = (2- (rho_s)/(rho ) )^(1//3) . h therefore A = 2 & B = 3, so A + B = 5 `