$A$ box of mass $15 \text{ kg}$ 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 a stationary state over the trolley, the maximum acceleration with which the trolley can be moved horizontally in $\text{m s}^{-2}$ is: $(g = 10 \text{m s}^{-2})$

$A$ body of weight $50 \,N$ is placed on a horizontal surface as shown in the figure. The minimum force required to move the body is $28.28 \,N$. The frictional force and the normal reaction are respectively.

$A$ heavy box is to be dragged along a rough horizontal floor. Person $A$ pushes it at an angle of $30^\circ$ from the horizontal and requires a minimum force $F_A$. Person $B$ pulls the box at an angle of $60^\circ$ from the horizontal and needs a minimum force $F_B$. If the coefficient of friction between the box and the floor is $\mu = \frac{\sqrt{3}}{5}$,find the ratio $\frac{F_A}{F_B}$.

Why is the coefficient of static friction considered a property of the surfaces in contact?

The maximum force of friction is called:

$A$ body of mass $m$ rests on a horizontal surface. The coefficient of friction between the body and the surface is $\mu$. If the mass is pulled by a force $P$ at an angle of $30^{\circ}$ with the horizontal as shown in the figure,the limiting friction between the body and the surface will be: