If the coefficient of friction is $\sqrt{3}$,what is the angle of friction between the two surfaces in contact (in $^{\circ}$)?

To avoid slipping while walking on ice,one should take smaller steps because of the

Explain: "Static friction force opposes impending motion".

If a pushing force making an angle $\alpha$ with the horizontal is applied on a block of mass $m$ placed on a horizontal table and the angle of friction is $\beta$,then the minimum magnitude of the force required to move the block is

As shown in the figure,a block of mass $\sqrt{3} \text{ kg}$ is kept on a horizontal rough surface with a coefficient of friction $\mu = \frac{1}{3 \sqrt{3}}$. $A$ force $F$ is applied on the vertical face of the block at an angle of $60^{\circ}$ with the horizontal. The minimum force $F$ required to just move the block is $3x$. Find the value of $3x$.
$\left[ g = 10 \text{ m/s}^2; \sin 60^{\circ} = \frac{\sqrt{3}}{2}; \cos 60^{\circ} = \frac{1}{2} \right]$

$A$ block of mass $4 \text{ kg}$ is placed on a horizontal surface having coefficients of static and kinetic friction as $0.5$ and $0.4$ respectively. If a force of $4 \text{ N}$ is applied parallel to the horizontal surface, then the force of friction acting on the body will be $\left[g = 10 \text{ m/s}^2\right]$ (in $\text{ N}$)