
The height of mercury barometer is h when the atmospheric pressure is , the pressure at x in the shown figure is
A.
B.
C.
D.

Answer
507k+ views
Hint: The above figure shows a setup of a static fluid. The horizontal surface of mercury will experience an exertion by the atmosphere. Pressure at point y can be calculated by formula of pressure. So by equating two equations for pressure at the horizontal surface we can easily encounter our answer.
As per the given data;
Height at which point x is situated
Atmospheric pressure Pa
Formula used:
Pressure,
Complete answer:
Hydrostatic pressure refers to the pressure exerted by a fluid (gas or liquid) at any point in space within that fluid, assuming that the fluid is incompressible and at rest.
Pressure within a liquid depends only on the density of the liquid, the acceleration due to gravity, and the depth within the liquid. The pressure exerted by such a static liquid increases linearly with increasing depth.
Mathematically;
Pressure,
Where, the pressure due to empty space or atmospheric formula
So pressure at the bottom surface of the glass tube of the barometer .will be;
(Assume that pressure due to the empty space in the glass tube is zero)
Let us see the pressure at y due to point x under the glass tube:
We know that, In case of static fluid, pressure on the horizontal level is constant at every point.
Thus;
By putting the value of :
So, the correct answer is “Option C”.
Note:
Read the question carefully. Remember that we don’t have to consider the whole height of the glass tube. Most importantly this is a static fluid setup so apply properties according to that only.
As per the given data;
Height at which point x is situated
Atmospheric pressure
Formula used:
Pressure,
Complete answer:
Hydrostatic pressure refers to the pressure exerted by a fluid (gas or liquid) at any point in space within that fluid, assuming that the fluid is incompressible and at rest.
Pressure within a liquid depends only on the density of the liquid, the acceleration due to gravity, and the depth within the liquid. The pressure exerted by such a static liquid increases linearly with increasing depth.
Mathematically;
Pressure,
Where,
So pressure at the bottom surface of the glass tube of the barometer
(Assume that pressure due to the empty space in the glass tube is zero)
Let us see the pressure at y due to point x under the glass tube:
We know that, In case of static fluid, pressure on the horizontal level is constant at every point.
Thus;
By putting the value of
So, the correct answer is “Option C”.
Note:
Read the question carefully. Remember that we don’t have to consider the whole height of the glass tube. Most importantly this is a static fluid setup so apply properties according to that only.
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