With what minimum velocity should a block be projected from the left end $A$ towards end $B$ such that it reaches the other end $B$ of a conveyor belt moving with a constant velocity $v$ towards the left? The length of the belt is $L$ and the coefficient of friction between the block and the belt is $\mu$.

$A$ block of mass $m$ (initially at rest) is sliding up a rough vertical wall with the help of a force $F$ whose magnitude is constant but direction is changing. $\theta = {\theta _0}t$,where $t$ is time in seconds. At $t = 0$,the force is in the vertical upward direction,and as time passes,its direction changes until $\theta = \frac{\pi }{2}$. The value of $F$ such that the block comes to rest when $\theta = \frac{\pi }{2}$ is:

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?

$A$ body of weight $50 \,N$ placed on a horizontal surface is just moved by a force of $28.2 \,N$ applied at an angle of $45^\circ$ with the horizontal. The frictional force and the normal reaction are

$A$ body is pulled along a rough horizontal surface with a velocity $6\,m/s$. If the body comes to rest after travelling $9\,m$,then the coefficient of sliding friction is- (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.