an open cubical tank was initally filled with water,if tank was accelerated on the horizantal plank along one of the side its1/3rd of volume spilled out.what is the acc of tank

Dear Jauneet Singh,

Ans:-The acc is a say. Then the pseudo force in the opposite direction is ma. where mis the mass of the fluid. Now due to this force V/3 amount of fluid has gone out. Thus from the given condition it is clear that the fluid layer in the tank is at a depth 1/3 rd of the total height when the tank is at rest. Now when it is moving with an acc a then it is not so. At that time the fluid will be in a triangular shape and the lowermost part of the fluid will be in the direction of the acc . Now from the simple geometry we can find that the bottom part will be at a height 2H/3 from the top. The angle between a and g(gravitational acc) is 90 degree let say θ be the angle of the hypotenouse with the horizental direction.. Then tanθ=a/g==2/3

Hence a=2g/3

N.B:- Geometrically tanθ should be the reverse but you can realize that is is happening as their effect are reverse i.e the effect of a acts vertically whereas effect of g hirizentally.

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