If the mass of block $A = 10\,kg$,the coefficient of static friction $\mu_s = 0.2$,and the coefficient of kinetic friction $\mu_k = 0.2$,find the mass of block $B$ required to start the motion.

$A$ body of mass $5 \,kg$ is placed on a rough horizontal surface of coefficient of static friction $\frac{1}{3}$. The least pulling force to be applied on the body at an angle $45^{\circ}$ with the horizontal to slide it,is . . . . . . $\left(g=10 \,ms^{-2}\right)$

As shown in the figure, a block of mass $10 \ kg$ lying on a horizontal surface is pulled by a force $F$ acting at an angle $30^{\circ}$ with the horizontal. For $\mu_{s} = 0.25$, the block will just start to move for the value of $F$: [Given $g = 10 \ ms^{-2}$] (in $N$)

$A$ heavy box is to be dragged along a rough horizontal floor. Person $A$ pushes it at an angle of $30^\circ$ from the horizontal and requires a minimum force $F_A$. Person $B$ pulls the box at an angle of $60^\circ$ from the horizontal and needs a minimum force $F_B$. If the coefficient of friction between the box and the floor is $\mu = \frac{\sqrt{3}}{5}$,find the ratio $\frac{F_A}{F_B}$.

If ${\mu _s}$,${\mu _k}$,and ${\mu _r}$ are coefficients of static friction,sliding (kinetic) friction,and rolling friction respectively,then:

$A$ body of mass $m$ is kept on a rough horizontal surface (coefficient of friction $= \mu$). $A$ horizontal force is applied on the body,but it does not move. The resultant of the normal reaction and the frictional force acting on the object is given by $F$,where $F$ is: