$A$ horizontal force just sufficient to move a body of mass $4 \,kg$ lying on a rough horizontal surface is applied on it. The coefficients of static and kinetic friction are $0.8$ and $0.6$ respectively. If the force continues to act even after the body has started moving, the acceleration of the body is (take $g=10 \,ms^{-2}$). (in $\,ms^{-2}$)

The limiting value of static friction between two contact surfaces is ...........

$A$ body of mass $2 \,kg$ is on an inclined plane of inclination $30^{\circ}$ and the coefficient of friction is $\frac{1}{\sqrt{3}}$. The minimum force required to move the body up the inclined plane is (Acceleration due to gravity $g = 10 \,ms^{-2}$) (in $\,N$)

If the normal force is doubled,the coefficient of friction is

$A$ 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 $\frac{F_A}{F_B}$.

$A$ pulling force $F$ making an angle $\theta$ with the horizontal is applied on a block of weight $W$ placed on a horizontal table. If the angle of friction is $\alpha$,then the magnitude of the force required to move the body is equal to