Question

Choose the wrong statement among the following
(This question has multiple correct options)
(A) The pressure at a point in a fluid is directly proportional to the depth of the point from the surface.
(B) The pressure at a point is independent of acceleration due to gravity.
(C) The pressure at a point is directly proportional to the area of the cross-section.
(D) The pressure at a point is proportional to the density of the fluid.

Answer 1

Hint : In this question, we have to select the wrong statement from the following options which options are based on the pressure. So we use the pressure equation to find out what statement is wrong and what statement is right.

Complete step by step answer: We are going to solve this question using different definitions and statements. Using these statements we can easily decide what is wrong or right.
Here, we are verifying statements one by one.
We can write pressure as $P=\rho gh$. Here $h$ is the depth from the surface.
So that means this statement is true because the pressure at a point in a fluid is directly proportional to the depth of the point from the surface.
We are using the same equation$p=\rho gh$. Here$g$is the acceleration due to gravity.
So according to this equation, this statement is true because the pressure at a point is directly proportional to the area of cross-section.
According to the equation$p=\rho gh$. In this equation, there is no role of cross-sectional area.
So according to this equation, this statement is wrong because the pressure at a point is not directly proportional to the area of cross-section.
According to the equation$p=\rho gh$. In this equation $\rho$is the density of the fluid.
So according to this equation, this statement is true because the pressure at a point is proportional to the density of the fluid.

So the answer is option C because option this statement is wrong.

Note: To understand this question we have to study this equation$p=\rho gh$. These all statements are based on this equation. In this statement, only one statement is wrong because there is no roll of the area in the pressure; it depends on the depth of the surface, acceleration due to gravity, or density of the fluid.