A large tank is filled with two liquids of specific gravities `2sigma` and `sigma`. Two holes are made on the wall of the tank as shown. Find the ratio of the distance from O of the points on the ground where the jets from holes A & B strike.

Answer

`sqrt(3):sqrt(2)`

Explanation

Velocity of efflux at `a V_(A)`
`DeltaP=(1)/(2)sigmav_(A)^(2)`
`V_(A)=sqrt((2DeltaP)/(sigma))" "impliesV_(A)=sqrt((2xx(h)/(4)xxsigmag)/(sigma))=sqrt((hg)/(2))`
time of flight
`t_(A)=sqrt((2xx(3h)/(4))/(g))=sqrt((3h)/(2g))`
For `V_(B)`
`V_(B)=sqrt((2(h)/(2)sigmag+(h)/(4)xx2sigmag))/(2sigma)impliesV_(B)=sqrt(hg)`
`t_(B)=sqrt((2xx(h)/(4))/(g))" "t_(B)=sqrt((h)/(2g))`
`(X_(A))/(X_(B))=(V_(A)xxt_(A))/(V_(B)xxt_(B))=sqrt((1)/(2))xxsqrt((3)/(1))implies(X_(A))/(X_(B))=sqrt((3)/(2))`