$A$ block of mass $3 \,kg$ is pressed against a vertical wall by applying a force $F$ at an angle $30^{\circ}$ to the horizontal as shown in the figure. As a result, the block is prevented from falling down. If the coefficient of static friction between the block and wall is $\mu = \sqrt{3}$, then the value of $F$ is (use $g=10 \,m/s^2$):

$A$ body of mass $2 \, kg$ moving on a horizontal surface with an initial velocity of $4 \, m/s$ comes to rest after $2 \, s$. If one wants to keep this body moving on the same surface with a constant velocity of $4 \, m/s$,the force required is ........ $N$.

$A$ block of mass $m=2 \ kg$ is initially at rest on a horizontal surface. $A$ horizontal force $F_1=(6 \ N) \hat{i}$ and a vertical force $F_2=(10 \ N) \hat{j}$ are then applied to the block. The coefficients of static friction and kinetic friction for the block and the surface are $0.4$ and $0.25$, respectively. The magnitude of the frictional force acting on the block is (assume $g=10 \ m/s^2$): (in $N$)

For the given figure,find the acceleration of the $40\, kg$ block in $m/s^2$. (Take $g = 10\, m/s^2$)

On a rough horizontal surface,a body of mass $2 \, kg$ is given a velocity of $10 \, m/s$. If the coefficient of friction is $0.2$ and $g = 10 \, m/s^2$,the body will stop after covering a distance of ........ $m$.

$A$ horizontal force of $40\,N$ is applied to a $5\,kg$ block which is at rest on a horizontal surface. If the coefficient of kinetic friction is $0.4$,then the acceleration of the block is ........ $m/s^2$ $(g = 10\,m/s^2)$.