$A$ 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 $\,ms^{-2}$)

As shown in the figure,a block of mass $\sqrt{3} \text{ kg}$ is kept on a horizontal rough surface with a coefficient of friction $\mu = \frac{1}{3 \sqrt{3}}$. $A$ force $F$ is applied on the vertical face of the block at an angle of $60^{\circ}$ with the horizontal. The minimum force $F$ required to just move the block is $3x$. Find the value of $3x$.
$\left[ g = 10 \text{ m/s}^2; \sin 60^{\circ} = \frac{\sqrt{3}}{2}; \cos 60^{\circ} = \frac{1}{2} \right]$

If the coefficient of friction is $\sqrt{3}$,what is the angle of friction between the two surfaces in contact (in $^{\circ}$)?

$A$ 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 $\,N$)

$A$ block of mass $m$ lying on a rough horizontal plane is acted upon by a horizontal force $P$ and another force $Q$ inclined at an angle $\theta$ to the vertical. The block will remain in equilibrium,if the coefficient of friction between it and the surface 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 $\frac{F_A}{F_B}$.