$A$ block of mass $10\, kg$ moving at $10\, m/s$ is released to slide on a rough surface having a coefficient of friction $0.2$. It will stop after travelling a distance of ........ $m$.

$A$ bag is gently dropped on a conveyor belt moving at a speed of $2\,m/s$. The coefficient of friction between the conveyor belt and the bag is $0.4$. Initially,the bag slips on the belt before it stops slipping due to friction. The distance travelled by the bag on the belt during the slipping motion is $.....m$. [Take $g=10\,m/s^{-2}$]

$A$ vehicle of mass $m$ is moving on a rough horizontal road with momentum $P$. If the coefficient of friction between the tyres and the road is $\mu$,then the stopping distance is:

$A$ 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 $g=10 \,m/s^2$):

$A$ rope of length $L$ and mass $M$ is being pulled on a rough horizontal floor by a constant horizontal force $F = Mg$. The force is acting at one end of the rope in the same direction as the length of the rope. The coefficient of kinetic friction between the rope and the floor is $1/2$. Then,the tension at the midpoint of the rope is

$A$ body of mass $20 \,kg$ is moving on a rough horizontal plane. $A$ block of mass $3 \,kg$ is connected to the $20 \,kg$ mass by a string of negligible mass through a smooth pulley as shown in the figure. The tension in the string is $27 \,N$. The coefficient of kinetic friction between the heavier mass and the surface is $\left(g=10 \,m/s^2\right)$.