As shown in the figure,a force $F$ is applied on a block of mass $\sqrt{3} \ kg$ placed on a rough horizontal surface. The maximum value of $F$ for the block not to move is (Coefficient of static friction between the block and the surface is $\mu = \frac{1}{2 \sqrt{3}}$ and acceleration due to gravity $g = 10 \ m \ s^{-2}$). (in $N$)

$A$ 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

For a given mass,how does rolling friction compare to static friction and kinetic friction?

If the normal force is doubled,the coefficient of friction is

$A$ person is using scissors to cut a wire of circular cross-section and negligible weight. The wire slides in the direction away from the hinge until the angle between the scissors blades becomes $2 \alpha$. The friction coefficient between the blades and the wire is:

$A$ body of mass $2 \,kg$ is on an inclined plane of inclination $30^{\circ}$ and the coefficient of friction is $\frac{1}{\sqrt{3}}$. The minimum force required to move the body up the inclined plane is (Acceleration due to gravity $g = 10 \,ms^{-2}$) (in $\,N$)