A liquid of density `rho` is filled in a beaker of cross section A to a height H and then a cylinder of mass M and cross-section a is made to float in it as shown in

If the atmospheric pressure is `P_0` find the pressure (a) at the top face B of the cylinder (b) at the bottom face C of the cylinder and (c ) at the base D of the beaker. (d) Can ever these pressure be equal ?

Explanation

(a) As the top face B of cylinder is in contact with atmospherice air, so the pressure at B is atmospheric pressure i.e. `P_B = P_0` (b) The pressure at C is due to atmospherice air and also de to weight of the cylinder, i.e., ` P_C = P_0 +(Mg)/(A)` (c ) The pressure at D is due to atmospheric air, weight of cylinder and weight of liquid in cylinder i.e., `P_D = P_0 + ((Mg + H rho g A))/(A) = P_0 + (Mg)/(A) + H rho g` (d) in the absence of gravity i.e., the system is in free fall (as is in satellite), then g =0 in this case `P_B = P_C = P_D = P_0.`