$A$ 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 $M$ is placed on a rough surface with a coefficient of friction $\mu = 3$. If the applied force $F$ is $(4/5)$ of the minimum force required to just move the block,find the total force exerted by the ground on the block.

As shown in the figure,a force $F$ is applied on a block of mass $\sqrt{3} \ kg$ placed on a rough horizontal surface. The maximum value of $F$ for the block not to move is (Coefficient of static friction between the block and the surface is $\mu = \frac{1}{2 \sqrt{3}}$ and acceleration due to gravity $g = 10 \ m \ s^{-2}$). (in $N$)

$A$ person initially at rest starts walking towards the east without slipping or skidding. What is the type of friction acting on the person from the ground,and in which direction does the frictional force act?

$A$ block of mass $50 \, kg$ can slide on a rough horizontal surface. The coefficient of friction between the block and the surface is $0.6$. The least force of pull acting at an angle of $30^\circ$ to the upward drawn vertical which causes the block to just slide is ........ $N$.

$A$ box of mass $2 kg$ is placed on the roof of a car. The box would remain stationary until the car attains a maximum acceleration. The coefficient of static friction between the box and the roof of the car is $0.2$ and $g=10 ms^{-2}$. This maximum acceleration of the car,for the box to remain stationary,is: (in $ms^{-2}$)