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Question

An open cubical container of side H is filled with a liquid up to height H4. Mass of liquid inside container is 'm' (neglect atmospheric pressure). When the container is moved with maximum possible acceleration without spilling water, what will be the magnitude of force applied by liquid on left wall parallel to plane of paper?

A
mg
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B
2mg
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C
mg3
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D
2mg3
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Solution

The correct option is B 2mg
Volume of liquid inside container is H34. When container is moved with maximum possible acceleration:
So,
volume of this triangular portion = H34
12H.x(H)=H34
x=H2

We know that, angle θ is given by:
tan θ=ag=Hx=2 a=2g

Force due to left wall is:
F=Pressure×Area
Now this pressure is varying from top to bottom, so we will take its average value from 0 to ρgH.

F=(0+ρgH)2.H2=ρgH32 [m=ρ(H34)]F=2g(ρH34)=2mg

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