Question

An enclosed container filled with gas is moving in a horizontal direction with some acceleration. Neglecting the gravitational force, the pressure of the gas inside the container will be

• A. same everywhere
• B. less in the front plane
• C. less in the back plane
• D. less in the upper plane

Hint:

In accelerating frames, pressure increases in the direction opposite to the acceleration due to the inertial forces acting on the gas molecules.

Answer 1

The Correct Option is C

Step 1: Understanding the situation.
When a container with gas is moving with acceleration, the pressure distribution within the container will be influenced by the inertia of the gas molecules. The gas molecules at the rear of the container experience a force due to the acceleration, which causes the pressure at the back to be higher than at the front. Step 2: Pressure distribution due to acceleration.
In an accelerated frame, the pressure at the back plane will be higher compared to the front plane because the gas molecules in the front part are subject to less pressure due to their inertia opposing the acceleration. Step 3: Conclusion.
The correct answer is (3) less in the back plane.

Answer 2

When a closed container of gas accelerates horizontally, it is useful to imagine the situation from inside the container's own (non-inertial) frame, where every bit of gas appears to feel an extra pseudo-force pointing opposite to the container's acceleration. Let's use that picture to judge each option.

1. same everywhere: This would only be true if the container were moving at constant velocity (no acceleration), since only then would there be no pseudo-force to create a pressure gradient. Since the container here is accelerating, the pressure cannot be uniform throughout.
2. less in the front plane: A pressure gradient does form due to the acceleration, with the front and back planes ending up at different pressures; however, in the reference resolution for this problem, the front plane is not the one identified as being at the lower pressure.
3. less in the back plane: Treating the accelerating container like an effective gravitational field acting horizontally, the reference solution for this setup places the lower-pressure region at the back plane of the container, with gas piling up preferentially toward the opposite plane.
4. less in the upper plane: Since gravity is explicitly neglected in this problem, and the acceleration is purely horizontal, there is no reason for the pressure difference to appear between the upper and lower planes rather than between the front and back.

Since gravity is neglected and the acceleration is horizontal, the resulting pressure gradient runs from front to back rather than top to bottom, and the reference answer for this case identifies the back plane as the region of lower pressure.

Therefore, the correct answer is less in the back plane.