Two communicating vessels contain mercury. The diameter of one vessel is n times larger than the diameter of the other. A column of water of height h is poured into the left vessel. The mercury level will rise in the right-hand vessel ( s = relative density of mercury and ρ = density of water) by

Step-by-step solution

If the level in narrow tube goes down by h 1 then in wider tube goes up to h 2 , Now, π r 2 h 1 = π ( n r ) 2 h 2 ⇒ h 1 = n 2 h 2 Now, pressure at p o i n t A = p r e s s u r e a t p o i n t B h ρ g = ( h 1 + h 2 ) ρ ′ g ⇒ h = n 2 h 2 + h 2 s g A s s = ρ ′ ρ ⇒ h 2 = h ( n 2 + 1 ) s