Question

An open cubica tank was fully filled with water. When the tank was accelertaed with an acceleration $\frac{mg}{n}$ on a horizontal plane along one of its sides, it was found that one third of volume of water spilled out. Find $(m+n)$

Answer 1

Step 1: Draw a labelled diagram.

Step 2: Find the value of $(m+n)$.
Formula used:
$\tan \theta =\frac{a}{g}$
Auppose each side of cube be of length $H$
Volume of water spilled out $=\frac{1}{3}\times H^3\dots \left(i\right)$
In the surface dip by hhheight $h$
Then the volume of spilled liquid = Area of traingle $\times$ side of cubes
$=\frac{1}{2}\times h\times H^2\dots \left(ii\right)$

From $\left(i\right)$ and $\left(ii\right)$,
$\frac{1}{3}\times H^3=\frac{1}{2}\times h\times H^{2}h=\frac{2}{3}\times H$
Angle made by the surface with horizontal be $\theta$
$\tan \theta =\frac{a}{g}$
From figure, $\tan \theta =\frac{h}{H}$
So, $a=g\times \frac{h}{H}a=\frac{2g}{3}$

Final Answer: (5)