A large cylindrical container with open top contains a liquid upto height `(2H=8m)` and whose density varies as shown in the figure. Atmospheric pressure is 1 atm `(=10^(5)N//m^(2))`
Find the pressure at botom of cylindrical container in atm.
(given `rho_(0)=10^(3)Kg//m^(2),` and `g=10m//s^(2)`)

Answer

2

Explanation

We have to calculate the partial pressure, generated due the liquid of variable density
`rho=(rho_(0))/Hy+rho_(0)`
`W=` weight of liquid column above the point `A`
`impliesW=int_(y)^(H)Srhogdy=gSrho_(0) int_(y)^(H)(1+y/H)dy`
`=gsrho_(0)[(H-y)+(H^(2)-y^(2))/(2H)]=(Srho_(0)(H-y)(3H-y)g)/(2H)`
`P_(1)=` Patial pressure at interface `(y=0)` due to liquid with variable density `=W/S|_(y=0)`
`=(3rho_(0)gH)/2`
`Pimplies` Pressure at bottom `=P_(0)+P_(1)+rho_(0)gH=rho_(0)+(5rho_(0)gH)/2`
`=10^(5)+(5xx10^(3)xx10xx4)/2=2xx10^(5)=2` atm