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 rope and floor is $1/2$ . Then, the tension at the midpoint of the rope is

A vehicle is moving with speed $v$ on a curved road of radius $r$. The coefficient of friction between the vehicle and the road is $\mu$. The angle $\theta$ of banking needed is given by

An isolated rail car originally moving with speed $v_0$ on a straight, frictionles, level track contains a large amount of sand. $A$ release valve on the bottom of the car malfunctions, and sand begins to pour out straight down relative to the rail car. What happens to the speed of the rail car as the sand pours out? 

......... $m/s^2$ is magnitude of acceleration of a block moving with speed $10\,m/s$ on a rough surface if coefficient of friction is $0.2$.

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

A body of mass m rests on horizontal surface. The coefficient of friction between the body and the surface is $\mu .$ If the mass is pulled by a force $P$ as shown in the figure, the limiting friction between body and surface will be