Figure shows a container filled with a liquid of density `rho`. Four points `A, B, C` and `D` lie on the vertices of a vertical square. Points `A` and `C` lie on a vertical line and points `B` and `D` lies on a horizontal line. Choose the correct statement(s) about the pressure at the four points.

Options

A. `P_(D)=P_(B)`
B. `P_(A)ltP_(B)=P_(D)ltP_(C)`
C. `P_(D)=P_(B)=(P_(C)-P_(A))/2`
D. `P_(D)=P_(B)=(P_(C)+P_(A))/2`

Answer

A, B, D

Explanation

According to Pascal's law
`P_(D)=P_(B)`
because `B` and `D` lie on the same horizontal plane.
Let `l` be the side of the square. Then the vertical distance between `A` and `C` is `lsqrt(2)`.
`P_(B)=P_(D)=P_(C)-rhogL/(sqrt(2))`………i
Similarly `P_(B)=P_(D)=P_(A)=rhogL/(sqrt(2))`...........ii
`P_(B)=P_(D)=(P_(A)+P_(C))/2`