Physics - NLM Question with Solution | TestHub

Let the acceleration of the trolley be $a$.

In the frame of the trolley, a pseudo force $ma$ acts on the box in the direction opposite to the motion.

For the box to remain stationary relative to the trolley, the static friction force must balance this pseudo force.

The maximum static friction force available is given by $f_{s,\text{max}}={\mu }_{s}N={\mu }_{s}mg$.

Equating the pseudo force to the maximum static friction force gives the maximum acceleration:

$m{a}_{\text{max}}={\mu }_{s}mg$

$a_{\text{max}}={\mu }_{s}g$

Substituting the given values ${\mu }_s=0.12$ and $g=10$ m/s${}^2$:

$a_{\text{max}}=0.12\times 10=1.2$ m/s${}^2$

Answer: $1.2$