$A$ body of mass $1 \, kg$ rests on a horizontal floor with which it has a coefficient of static friction $\frac{1}{\sqrt{3}}$. It is desired to make the body move by applying the minimum possible force $F \, N$. The value of $F$ will be (Nearest Integer). [Take $g = 10 \, m s^{-2}$]

$A$ 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 $\frac{F_A}{F_B}$.

$A$ force $F = mg$ is acting on a block of mass $m$ at an angle $\theta$ with the horizontal. The coefficient of friction between the block and the surface is $\mu$. The block can be pulled along the surface if:

$A$ pulling force $F$ making an angle $\theta$ with the horizontal is applied on a block of weight $W$ placed on a horizontal table. If the angle of friction is $\alpha$,then the magnitude of the force required to move the body is equal to

$A$ block of mass $M$ rests on a rough horizontal table. $A$ steadily increasing horizontal force is applied such that the block starts to slide on the table without toppling. The force is continued even after sliding has started. Assume the coefficients of static and kinetic friction between the table and the block to be equal. The correct representation of the variation of the frictional force $f$,exerted by the table on the block with time $t$ is given by

$A$ block of mass $70\,kg$ is kept on a rough horizontal surface $(\mu = 0.4)$. $A$ person is trying to pull the block by applying a horizontal force,but the block is not moving. The net contact force exerted by the surface on the block is $F$,then