The vessel shown in the figure has two sections. The lower part is a rectangular vessel with area of cross-section A and height h. The upper part is a conical vessel of height h with base area A and top area `a` and the walls of the vessel are inclined at an angle `30^(@)` with he vertical.A liquid of density `rho` fills both the sections upto a height 2h. Neglect atmospheric pressure.

Options

A. The force F exerted by the liquid on the base of the vessel is `2hrho g.((A+a))/(2)`
B. the pressure P at the base of the vessel is `2hrhog.(A)/(a)`
C. the weight of the liquid W is greater than the force exerted by the liquid on the base
D. the walls of the vessel exert a downward force `(F-W)` on the liquid.

Answer

D

Explanation

`F-PA`
`F=2hrhog.A`
`W+f_(y)=F`
By taking free body diagram of liquid
`f_(y)=F-W`
so option (D) is correct.