A box of mass 15 kg is kept on the floor of a stationary trolley. The coefficient of static friction between the box and the trolley is 0.12. Keeping the box in stationary state over the trol ley, the maximumacceleration with which the trolley can be movedhorizontally in m s² is: ____.

Given data:

Mass of the box, $m\; =\; 15 kg$.
Coefficient of static friction between the box and the trolley, $\backslash mu\_s\; =\; 0.12$.
Acceleration due to gravity, $g\; =\; 9.8 m s⁻²$.

The normal reaction exerted by the trolley on the box equals the weight of the box because the motion is horizontal:

$N\; =\; m g\; =\; 15 \times 9.8\; =\; 147 N$

The largest possible static‑friction force that can act on the box is

$f\_\{\backslash text\{max\}\}\; =\; \backslash mu\_s N\; =\; 0.12 \times 147\; =\; 17.64 N$

When the trolley accelerates, the box must be accelerated together with it. The required horizontal force on the box is provided solely by static friction, so

$f\_\{\backslash text\{max\}\}\; =\; m a\_\{\backslash text\{max\}\}$

Solving for the maximum allowable acceleration:

$a\_\{\backslash text\{max\}\}\; =\; \backslash frac\{f\_\{\backslash text\{max\}\}\}\{m\}\; =\; \backslash frac\{17.64\}\{15\}\; =\; 1.176 m s⁻²$

Rounding to one decimal place (consistent with the given options) gives

$a\_\{\backslash text\{max\}\}\; \approx \; 1.2 m s⁻²$

Therefore the trolley can be accelerated horizontally up to approximately 1.2 m s⁻² without the box slipping.