A container of large uniform cross – sectional area holds two immiscible, non – viscous and incompressible liquids of densities ρ and 4ρ , each of height H2 . Determine the position where, a small hole has to be punched, so that the heavier liquid comes out with a maximum range R initially.
see full answer
Your Exam Success, Personally Taken Care Of
1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.
An Intiative by Sri Chaitanya
a
At a height H4 from the bottom
b
At a height 54H from the bottom
c
At a height 516H from the bottom
d
At a height 718H from the bottom
answer is C.
(Unlock A.I Detailed Solution for FREE)
Best Courses for You
JEE
NEET
Foundation JEE
Foundation NEET
CBSE
Detailed Solution
On applying Bernoulli’s theorem between points (1) and (2), we havep0+ρgH2+4ρg(H2−h)=p0+124ρu2ρgH2+2ρgH−4ρgh=2ρu25ρgH2−4ρgh=2ρu2 ⇒u2=[54gH−2gh]⇒u2=g4[5H−8h] ⇒u=g25H−8h t=2hgR=ut=g25H−8h.2hg=125Hh−8h2For R to be maximum,dRdh=0 dRdh=12.125Hh−8h2(5H−16h)=0⇒5H−16h=0 ⇒h=516H