$A$ 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 $g=10\,m/s^{-2}$]

The coefficient of friction between the block of mass ${M_1}$ and the surface is $\mu$. When the system is released,it moves with acceleration. What mass $m$ should be placed on the block ${M_1}$ so that the system moves with a constant velocity?

$A$ block of mass $\sqrt{2} \,kg$ is placed on a rough horizontal surface. $A$ force $F$ acting upwards at an angle of $45^{\circ}$ with the horizontal causes the block to start motion. If the coefficient of static friction between the surface and the block is $0.25$, the magnitude of the force $F$ is (Acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,N$)

$A$ man slides down a telegraphic pole with an acceleration equal to one-fourth of the acceleration due to gravity. The frictional force between the man and the pole is equal to which of the following in terms of the man's weight $w$?

$A$ block of $7\,kg$ is placed on a rough horizontal surface and is pulled by a variable force $F$ (in $N$) $= 5t$,where $t$ is time in seconds,at an angle of $37^{\circ}$ with the horizontal as shown in the figure. The coefficient of static friction between the block and the surface is $\mu = 1$. If the force starts acting at $t = 0\,s$,find the time at which the block starts to slide. (Take $g = 10\,m/s^2$)

$A$ horizontal force of $4\,N$ is needed to keep a block of mass $0.5\,kg$ sliding on a horizontal surface with a constant speed. The coefficient of sliding friction must be: $[g = 10\,m/s^2]$