$A$ stationary body of mass $m$ is slowly lowered onto a massive platform of mass $M$ $(M \gg m)$ moving at a speed $V_p = 4 \, m/s$ as shown in the figure. How far will the body slide along the platform (in $, m$)? (Given: $\mu = 0.2$ and $g = 10 \, m/s^2$)

$A$ fireman of mass $60 \ kg$ slides down a pole. He is pressing the pole with a force of $600 \ N$. The coefficient of friction between the hands and the pole is $0.5$. With what acceleration (in $m/s^2$) will the fireman slide down? (Take $g = 10 \ m/s^2$)

$A$ uniform rod of length $L$ and mass $M$ is placed on a rough horizontal surface. $A$ horizontal force $F$ is applied at one end of the rod such that the rod is just in the state of rest. The coefficient of friction varies according to the relation $\mu = Kx$,where $K$ is a positive constant and $x$ is the distance from the end where the force is not applied. Find the tension at the midpoint of the rod.

$A$ block of mass $5 \,kg$ moving on a rough surface with a velocity of $4 \,ms^{-1}$ is stopped by friction in $2 \,s$. The coefficient of friction between the contact surfaces is (Acceleration due to gravity $g = 10 \,ms^{-2}$)

$A$ spring-block system is placed on a rough horizontal floor. The block is pulled towards the right to give the spring some elongation and then released. The block will have maximum velocity when:

What is the maximum value of the force $F$ such that the block shown in the arrangement does not move? (in $N$)