For the equilibrium of a body on an inclined plane of inclination $45^{\circ}$, the coefficient of static friction must be:

The coefficient of friction between two surfaces is $\mu = 0.8$. The tension in the string shown in the figure is ........ $N$.

The force required to move a body up a rough inclined plane is double the force required to prevent the body from sliding down the plane. The coefficient of friction,when the angle of inclination of the plane is $60^{\circ}$ is

$A$ cone of radius $r$ and height $h$ rests on a rough horizontal surface,the coefficient of friction between the cone and the surface being $\mu$. $A$ gradually increasing horizontal force $F$ is applied to the vertex of the cone. The largest value of $\mu$ for which the cone will slide before it topples is

In the figure,two blocks $M$ and $m$ are tied together with an inextensible and light string. The mass $M$ is placed on a rough horizontal surface with a coefficient of friction $\mu$,and the mass $m$ is hanging vertically. The pulley is frictionless. Choose the correct statement$(s)$.

Two blocks $A$ and $B$ of equal masses are sliding down along straight parallel lines on an inclined plane of $45^{\circ}$. Their coefficients of kinetic friction are $\mu_A = 0.2$ and $\mu_B = 0.3$ respectively. At $t = 0$,both the blocks are at rest and block $A$ is $\sqrt{2} \text{ m}$ behind block $B$. Calculate the time and distance from the initial position where the front faces of the blocks come in line on the inclined plane as shown in the figure. (Use $g = 10 \text{ m/s}^2$)