Question

A box of dimensions $l\times b$ is kept on a truck moving with an acceleration $a$. If the box does not slide, maximum acceleration of the truck for it to remain in equilibrium (w.r.t. the truck) is

• A. $\frac{gl}{b}$
• B. $\frac{gb}{l}$
• C. $g$
• D. None of these

Answer 1

The correct option is B $\frac{gb}{l}$

$FBD$ of the box from its frame of reference. We have to consider pseudo force $ma$ to the left.


When the box is just about to topple, normal reaction will shift to the edge.

Hence, from torque balance about point $\text{O}$.
$ma\times \left(\frac{l}{2}\right)=mg\left(\frac{b}{2}\right)$
or $a=\frac{gb}{l}$