$A$ body of mass $10 \ kg$ slides along a rough horizontal surface. The coefficient of friction is $1/\sqrt{3}$. Taking $g = 10 \ m/s^2$,the least force which acts at an angle of $30^\circ$ to the horizontal is ...... $N$.

$A$ block placed on a rough horizontal surface is pulled by a horizontal force $F$. Let $f$ be the force applied by the rough surface on the block. Plot a graph of $f$ versus $F$.

$A$ body of mass $1 \, kg$ rests on a horizontal floor with which it has a coefficient of static friction $\frac{1}{\sqrt{3}}$. It is desired to make the body move by applying the minimum possible force $F \, N$. The value of $F$ will be (Nearest Integer). [Take $g = 10 \, m s^{-2}$]

The maximum value of the applied force $F$ such that the block as shown in the arrangement does not move is (Acceleration due to gravity, $g=10 \,ms^{-2}$) (in $\,N$)

$A$ block of mass $M$ is held against a rough vertical wall by pressing it with a finger. If the coefficient of friction between the block and the wall is $\mu$ and the acceleration due to gravity is $g$,calculate the minimum force required to be applied by the finger to hold the block against the wall.

$A$ force $\vec{F}=\hat{i}+4 \hat{j} \, N$ acts on the block of mass $1 \, kg$ shown in the figure. The coefficient of friction between the block and the surface is $\mu = 0.3$. The force of friction acting on the block is (Take $g = 10 \, m/s^2$)