0

Guest

Courses New

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
10 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
6 years ago
Uddijd saath vs ygadhuscjisarhjmfawh has g had is by Takahashi habitability to kanaksusunher kaleidoscope clairaudience dissociation
Kushagra Madhukar
askIITians Faculty 628 Points
3 years 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

Think You Can Provide A Better Answer ?

Other Related Questions on Mechanics

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More