Question

An open cubical tank completely filled with water is kept on a horizontal surface. Its acceleration is then slowly increased to $2m/s^2$ as shown in the fig. The side of the tank is $1m$. The mass of water that would spill out of the tank in kg is 20×X , then the value of x is

Answer 1

Let the water form an angle of $\theta$ with the horizontal in pseudo equilibrium.

Resolving the components of gravitational force and pseudo force along the water surface,

$a\cos \theta =g\sin \theta$

$⟹\tan \theta =\frac{a}{g}=0.2$

Thus volume of the water spilled out of this vessel due to backward extending triangle formed void $=\frac{1}{2}\times (1m\times \tan \theta )\times 1m\times 1m=0.1m^3$

Weight of this water $=100kg$