Fluids at rest exert a normal force to the walls of the container or to the sruface of the body immersed in the fluid. The pressure exerted by this force at a point inside the liqid is the sum of atmospheric pressure and a factor which depends on the density of the liquid, the acceleration due to gravity and the height of the liquid, above that point. The upthrust acting on a body immersed in a stationary liquid is the net force acting on the body in the upward direction. A number of phenomenon of liquids in motion can be explain by Bernoulli's theorem which relates the pressure, flow speed and height for flow of an ideal incompressible fluid.
A container of large uniform corss sectional area. A resting on a horizontal surface holds two immiscible, non viscous and incompressile liquids of densities `d` and `2d`, each of height `H//2` as shown in the figure. The lower density liquid is open to the atmosphere having pressure `P_(0)`.
Situation I:
A homogeneous solid cylinder of length `L(LltH//2)`. cross sectional area `A//5` is immersed such that it floats with its axis vertical at liquid -liquid interface with lenght `L//4` in the denser liquid.
The total pressure at the bottom of the container is

Options

A. `(H/2+L/4)dg`
B. `P_(0)+((3H)/2+L/2)dg`
C. `P_(0)+(H+L/4)dg`
D. `P_(0)+((3H)/2+L/4)dg`

Answer

D

Explanation

Total pressure at the bottom is
`P=P_0+(["weight of" ("liquid" + "object")])/A`
`implies P=P_0+([(AH)/2dg+(AH)/22dg+A/5L(5d)/4g])/A`
`implies P=P_0+((3H)/2+L/4)dg`