$A$ 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 $\,N$)

$A$ 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 $10 \ kg$ lying on a horizontal surface is pulled by a force $F$ acting at an angle $30^{\circ}$ with the horizontal. For $\mu_{s} = 0.25$, the block will just start to move for the value of $F$: [Given $g = 10 \ ms^{-2}$] (in $N$)

If a ladder weighing $250\,N$ is placed against a smooth vertical wall and the coefficient of friction between the ladder and the floor is $0.3$,what is the maximum force of friction available at the point of contact between the ladder and the floor?

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 $5 \,kg$ is placed on a rough horizontal surface of coefficient of static friction $\frac{1}{3}$. The least pulling force to be applied on the body at an angle $45^{\circ}$ with the horizontal to slide it,is . . . . . . $\left(g=10 \,ms^{-2}\right)$