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On an inclined plane there is a beaker filled with fluid, what will be the shape of fluid as the beaker accelerates down? What I think is that the beaker accelerates with $g \sin\theta$ acceleration down the incline and so does the fluid molecules of surface, so fluid molecules experience a net real force down the incline of $mg\sin\theta$, and $mg\cos \theta$ perpendicular to the inclined plane due to $mg$ component, so the net force is $mg$ down only, and fluid should take a horizontal shape (perpendicular to net force) but as I have seen answer isn't this, the solution takes into consideration a pseudo force.I don't get where my method is wrong, isn't fluid perpendicular to real force?

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    $\begingroup$ Hi. Please try and use Latex for rendering formulas/math. For simple formulas include them between $ signs. Also, draw an FBD to see the light in this simple problem. $\endgroup$
    – Gert
    Commented Nov 26, 2021 at 11:31
  • $\begingroup$ Ok, I am new here so didn't knew latex worked here also. I have added the diagram of what I expect can u check pls $\endgroup$
    – Math-Wiz
    Commented Nov 26, 2021 at 11:37

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It's a confusing question, but the net force on the fluid must be down the plane, otherwise the fluid would accelerate straight downwards through the plane.

There is also the normal reaction force from the bottom of the beaker of value $mg\cos\theta$, so the resultant force on the fluid is the $mg\sin\theta$ component going down the plane.

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  • $\begingroup$ Why won't a water molecule at surface have acc. Perpendicular to plane, can't it go in, like ir that the molecules keep on going in the fluid and below molecules come up etc, also idt fluid molecules apply normal on one another $\endgroup$
    – Math-Wiz
    Commented Nov 26, 2021 at 11:57
  • $\begingroup$ @ Math-Wiz, the ones beneath can't go anywhere so there is a pressure throughout the liquid that keeps even the higher ones from accelerating straight down, sorry not sure what all the abbreviations mean! $\endgroup$
    – John Hunter
    Commented Nov 26, 2021 at 12:02
  • $\begingroup$ Still no clear, if one could explain it better, describe what's this extra force between molecules it would be better, idk why taking a psuedo force of mgsinø and real force mg works and not this $\endgroup$
    – Math-Wiz
    Commented Nov 26, 2021 at 12:14
  • $\begingroup$ @ Math-Wiz it's a similar force to when the beaker is on a table, the molecules don't move down through the bottom of the beaker, the downward force of gravity is balanced by the reaction force from the bottom of the beaker. Got to stop now, all the best with it. $\endgroup$
    – John Hunter
    Commented Nov 26, 2021 at 12:30
  • $\begingroup$ I still don't get it, fluid molecules can exert normal forces ? When we do the pseudo force solution then also we don't take normal, but still the answer comes. If someone can clarify it better it would be nice $\endgroup$
    – Math-Wiz
    Commented Nov 26, 2021 at 15:11
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I don't know what $d$ refers to, but the total acceleration is $g \sin{\theta}$ down the ramp. There is a vertical component and a horizontal component. As someone stated, the vertical component does not affect the liquid angle. The horizontal component of $g \sin{\theta}$ is $g \sin{\theta} \cos{\theta}$. So the effect is similar to jerking the beaker sideways. You can verify for yourself with a mug of coffee (and some paper towels) that the level angle will change if you do this.

It's true that one should get the same answer regardless of approach, but trying to do problems with "pseudo-forces" tends to cause confusion. A force is a force and an acceleration is an acceleration. I would encourage you to draw free body diagrams and apply $F=ma$.

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