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An oil tanker is partially filled and is then moved in translation at uniform acceleration. The free surface of oil then
  • a)
    remains horizontal
  • b)
    is inclined to horizontal with smaller depth at the rear end
  • c)
    is inclined such that a larger depth occurs at the rear end
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
An oil tanker is partially filled and is then moved in translation at ...
In this case the surface of constant pressure is a downward sloping plane surface. The free surface of the liquid is a surface of cohstant pressure, because the pressure at the free surface is equal to atmospheric pressure which is constant. As such under the effect of the horizontal acceleration the free surface of the liquid will become a downward sloping inclined plane, with the liquid rising at the back end and the liquid falling at the front end.
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An oil tanker is partially filled and is then moved in translation at ...
Explanation:
When an oil tanker is partially filled and moved in translation at uniform acceleration, the free surface of the oil in the tanker will be inclined such that a larger depth occurs at the rear end. This can be explained using the principles of fluid mechanics.

Fluid Mechanics:
Fluid mechanics deals with the behavior of fluids (liquids and gases) at rest and in motion. When a fluid is in motion, it exerts pressure on its surroundings. This pressure depends on the depth of the fluid and the acceleration experienced by the fluid.

Free Surface of Oil:
The free surface of the oil refers to the boundary between the oil and the surrounding atmosphere. In the case of an oil tanker, the free surface of the oil is exposed to the atmosphere.

Uniform Acceleration:
When the oil tanker is moved in translation at uniform acceleration, the oil inside the tanker experiences an acceleration. This acceleration is transmitted to the free surface of the oil.

Effects of Acceleration:
The acceleration experienced by the fluid causes a pressure gradient within the fluid. This pressure gradient results in the inclination of the free surface of the oil.

Inclination of Free Surface:
The free surface of the oil will be inclined such that a larger depth occurs at the rear end of the tanker. This means that the rear end of the tanker will have a greater depth of oil compared to the front end.

Reasoning:
The reason for this inclination is that the fluid particles near the rear end of the tanker experience a greater acceleration compared to the fluid particles near the front end. As a result, the pressure near the rear end is higher than the pressure near the front end. This pressure difference causes the free surface of the oil to be inclined, with a larger depth at the rear end.

Conclusion:
In summary, when an oil tanker is partially filled and moved in translation at uniform acceleration, the free surface of the oil is inclined such that a larger depth occurs at the rear end. This is due to the pressure difference caused by the acceleration experienced by the fluid particles.
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An oil tanker is partially filled and is then moved in translation at uniform acceleration. The free surface of oil thena)remains horizontalb)is inclined to horizontal with smaller depth at the rear endc)is inclined such that a larger depth occurs at the rear endd)None of theseCorrect answer is option 'C'. Can you explain this answer?
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