As shown in the figure, a liquid is at the same levels in two arms of a U-tube of uniform cross-section when at rest. If the U-tube moves with an acceleration 'f' towards the right,the difference in liquid heights between the two arms of the U-tube will be,(acceleration due to gravity=g)
- \(\frac{f}{g}a\)
- \(\frac{g}{f}a\)
- a
- 0
The Correct Option is A
Approach Solution - 1
Given pressures P1 and P2 at the bottom of the left and right ends of the tube respectively, the force F can be expressed as the difference between the pressures multiplied by the cross-sectional area A, which is F=(P1−P2)A=ρghA.
The mass of the liquid in the horizontal portion is represented as m=ρLA. Substituting this into F=ma gives us ρghA=ρLAa.
Hence, the answer is f/g=a.
The correct answer is option (A): \(\frac{f}{g}a\)
Approach Solution -2
Given pressures P1 and P2 at the bottom of the left and right ends of the tube respectively, the force F can be expressed as the difference between the pressures multiplied by the cross-sectional area A, which is:
F = (P1 − P2) A = ρghA
The mass of the liquid in the horizontal portion is represented as:
m = ρLA
Substituting this into F = ma gives us:
ρghA = ρLAa
Hence, the answer is:
f/g = a
The correct answer is option (A): f/g = a
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Concepts Used:
Mechanical Properties of Fluid
The science of the mechanical properties of fluids is called Hydrostatics. A fluid is a substance that relents to the slightest pressure. Fluids are categorized into two classes famed by the names of liquids, and elastic fluids or gases, which later comprehend the air of the atmosphere and all the different kinds of air with which chemistry makes us acquainted.
Streamline Flow:
A streamline is a curve the tangent to which at any point provides the direction of the fluid velocity at that point. It is comparable to a line of force in an electric or magnetic field. In steady flow, the pattern of the streamline is motionless or static with time, and therefore, a streamline provides the actual path of a fluid particle.
Tube of Flow:
A tubular region of fluid enclosed by a boundary comprises streamlines is called a tube of flow. Fluid can never cross the boundaries of a tube of flow and therefore, a tube of flow acts as a pipe of the same shape.
Surface Tension and Viscosity:
The surface tension of a liquid is all the time a function of the solid or fluid with which the liquid is in contact. If a value for surface tension is provided in a table for oil, water, mercury, or whatever, and the contacting fluid is unspecified, it is safe to consider that the contacting fluid is air.
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