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

Question

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 <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-tolsfp84bxbz.png" /> (A) (n2 h/(n+1)2 s) (B) (h/(. n2 + 1 .) s) (C) (h/(n+1)2 s) (D) (h/n2 s)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-tolsfp84toeu.png" /> If the level in narrow tube goes down by h1 then in wider tube goes up to h2 Now, π r2 h1=π(n r)2 h2 ⇒ h1=n2h2 Now, pressure at point A = pressure at point B hρ g=(.h1+h2.)ρ'g ⇒ h =(n2 h2 + h2)sg(A s s = ((ρ )'/ρ )) ⇒ h2=(h/(. n2 + 1 .) s)

$\frac{n ^{2} h}{( n + 1 ) ^{2} s}$

$\frac{h}{( n ^{2} + 1 ) s}$

$\frac{h}{( n + 1 ) ^{2} s}$

$\frac{h}{n ^{2} s}$

(n+1)2sn2h​

(n2+1)sh​

(n+1)2sh​

n2sh​

If the level in narrow tube goes down by h1​ then in wider tube goes up to h2​ Now, πr2h1​=π(nr)2h2​ ⇒h1​=n2h2​ Now, pressure at point A= pressure at point B hρg=(h1​+h2​)ρ′g ⇒h=(n2h2​+h2​)sg(Ass=ρ(ρ)′​) ⇒h2​=(n2+1)sh​

$\frac{n ^{2} h}{( n + 1 ) ^{2} s}$

$\frac{h}{( n ^{2} + 1 ) s}$

$\frac{h}{( n + 1 ) ^{2} s}$

$\frac{h}{n ^{2} s}$