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An open cubical tank was initially fully filled with water. when the tank was accelerated on a horizontal plane along one of its sides, 1/3rd volume of water spilled out. The acceleration is?

An open cubical tank was initially fully filled with water. when the tank was accelerated on a horizontal plane along one of its sides,  1/3rd volume of water spilled out. The acceleration is?

Grade:12

3 Answers

Nirmal Singh.
askIITians Faculty 44 Points
7 years ago
Let
L = length of the container
B = breadth of the container
H = height of the container
as container is a cube.
so, L = B = H
We know that angle made by free surface with the horizontal is given by tan ? = a/g
where a = acceleration of the container in the horizontal direction
Now we can see that there are sides of the container when seen from the side. These are front side and rear side.
When the container is accelerating then the water level on the front side will come down and the water level in the rear side will go up.

The container was completely filled with water so the amount of water that will rise in the rear side will go out or will spill out. so. the water level in the rear side will remain constant because it cannot increase more.
tan ? = h/L
where h = fall in water level on the front side.
L = length of the container
h = L tan ?
Now volume of the free space above the water level after spilling =
(1/2) x h x L x B
This volume is equal to amount of water spilled out.
Total volume of container - L x B x H
Ratio = (h x L x B)/(2 x L x B x H) = h/2H = 1/3
h = H - L tan ? = H( 1 - tan ?)
h/2H = (1 - tan ?)/2 = 1/3
tan ? = 1/3 = a/g
a = g/3
Bhawna Chugh
19 Points
3 years ago
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Kushagra Madhukar
askIITians Faculty 629 Points
one year ago
Dear student,
Please find the attached solution to your problem.
 
The initial volume of tank, V =  L3
where A is the area of base of tank and L is its height.
 
As we know,
tanθ = a/g
Final volume, V’ = L2 x (L – Ltanθ) + ½ x L x Ltanθ x L
                        = L3 – L3tanθ + L3tanθ/2
                        = L3 – L3tanθ/2
Volume spilled = V – V’ = L3tanθ/2 = L3/3
Hence, tanθ = 2/3
Therefore, a = g*tanθ = 2/3g
 
Hope it helps.
Thanks and regards,
Kushagra

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