Determine the maximum acceleration in $m/s^2$ of the train in which a box lying on its floor will remain stationary, given that the co-efficient of static friction between the box and the train’s floor is $0.15.$

A block of mass $2\,kg$ moving on a horizontal surface with speed of $4\,ms ^{-1}$ enters a rough surface ranging from $x =0.5\,m$ to $x =1.5\,m$. The retarding force in this range of rough surface is related to distance by $F =- kx$ where $k =12\,Nm ^{-1}$. The speed of the block as it just crosses the rough surface will be ........... $\,ms ^{-1}$

A block of mass $m$ (initially at rest) is sliding up (in vertical direction) against 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 sec. At $t$ = $0$ , the force is in vertical upward direction and then as time passes its direction is getting along normal, i.e., $\theta  = \frac{\pi }{2}$ .The value of $F$ so that the block comes to rest when $\theta  = \frac{\pi }{2}$ , is 

A heavy box is to dragged along a rough horizontal floor. To do so, person $A$ pushes it at an angle $30^o$ from the horizontal and requires a minimum force $F_A$, while person $B$ pulls the box at an angle $60^o$ from the horizontal and needs minimum force $F_B$. If the coefficient of friction between the box and the floor is $\frac{{\sqrt 3 }}{5}$ , the ratio $\frac{{{F_A}}}{{{F_B}}}$ is

When a body slides down from rest along a smooth inclined plane making an angle of $45^o$ with the horizontal, it takes time $T$. When the same body slides down from rest along a rough inclined plane making the same angle and through the same distance, it is seen to take time $pT$, where $p$ is some number greater than $1$. Calculate the coefficient of friction between the body and the rough plane.

A force $f$ is acting on a block of mass $m$. Coefficient of friction between block and surface is  $\mu$. The block can be pulled along the surface if :-