$A$ uniform rope of length $l$ lies on a table. If the coefficient of friction is $\mu$,then the maximum length $l_1$ of the part of this rope which can overhang from the edge of the table without sliding down is

$A$ block of mass $10\, kg$ is kept on a rough inclined plane as shown in the figure. $A$ force of $3\, N$ is applied on the block directed down the plane. The coefficient of static friction between the plane and the block is $0.6$. What should be the minimum value of force $P$ applied up the plane,such that the block does not move downward (in $, N$)? (Take $g = 10\, ms^{-2}$)

$A$ block of mass $10 \ kg$, initially at rest, makes a downward motion on a $45^{\circ}$ inclined plane. The distance travelled by the block after $2 \ s$ is (Assume the coefficient of kinetic friction to be $0.3$ and $g=10 \ m/s^2$)

$A$ particle is projected up along a rough inclined plane of inclination $45^{\circ}$ with the horizontal. If the coefficient of friction is $0.5$,the acceleration is ($g=$ Acceleration due to gravity).

The tension $T$ in the string shown in the figure is ..................... $N$.

The upper half of an inclined plane with an angle of inclination $\phi$ is smooth,while the lower half is rough. $A$ body starting from rest at the top of the inclined plane comes to rest at the bottom of the inclined plane. Then the coefficient of friction for the lower half is