Question

A cubical box is filled 50% with water and is open from upper part, then it is fixed on a moving cart with an acceleration 'a' on a fixed inclined as shown in figure. Value of 'a' for which water will not come out from cube is:

• A. $\frac{g}{2}$
• B. $g$
• C. $2g$
• D. $3g$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A $2g$
B $g$
C $\frac{g}{2}$
D $3g$

The acceleration in the horizontal direction is $asin{45}^o$ and in the vertical direction is $g+acos{45}^o$.
Now as the water is in the cubical box, it will spill out of the box when $tan\varphi >\frac{g+acos{45}^o}{asin{45}^o}$.
Here $\varphi$ is the angle made by the water level when it starts to spill out of the box. As the box is cubical, this angle is ${45}^o$.
Solving this equation we see that $a$ and $g$ are independent of each other.
This implies that for any value of acceleration the water will not spill out of the box. It may reach upto a maximum height of the box.