Question

Two drums of the same size and same height are taken.

i)what will be the difference in liquid pressure on their bases if A of them is completely filled and B is half filled and kept at the same place.
ii) what will be the difference in liquid pressure on their bases if both A and B are filled with water completely but one of them is kept at nepal and another in india?why?
iii) what will be the difference in liquid pressure on their bases if A is filled with water and B is filled with salty water and kept at delhi in the same position?why?​

Answer 1

i) The pressure acting on the base of B will be half the pressure acting on the base of A

ii) The pressure acting on the base of B will be the same as the pressure acting on the base of A

iii) The pressure on the base of drum A will be slightly less than the pressure on the base of drum B

Step-by-step explanation:

The pressure acting on the base of the drum, P = h·ρ·g

Where;

h = The level of the liquid in the drum

`h_(max)` = The height of the drums

ρ = The density of the liquid in the drum

g = The acceleration due to gravity ≈ 9.81 m/s²

i) If A is completely filled, we have
`h_A` =
`h_(max)`

Therefore,
`P_A` =
`h_(max)`×
`\rho_(liquid)`×g

If B is half filled, we have,
`h_B` = (1/2)·
`h_(max)`

`P_B` = (1/2) ×
`h_(max)`×
`\rho_(liquid)`×g

Therefore,
`P_B` = (1/2) ×
`P_A`

The pressure acting on the base of B will be half the pressure acting on the base of A

ii) If both A and B are each filled with water (the same liquid), then the pressure on their bases will be
`P_A` =
`h_(max)`×
`\rho_(water)`×g =
`P_B`, the same, given that the acceleration due to gravity, g, is constant and the same in Nepal and India

iii) If A is filled with water, and B is filled with salty water, we have that, the density of salty water is slightly higher than water, therefore, we get;

`P_A` =
`h_(max)`×
`\rho_(water)`×g <
`P_B` =

The pressure on the base of drum A will be less than the pressure on the base of drum B.