$A$ uniform rope lies on a horizontal table such that a part of it hangs over the edge. The rope begins to slide down when the length of the hanging part is $25\%$ of its entire length. The coefficient of friction between the rope and the table is

$A$ force of $750 \, N$ is applied to a block of mass $102 \, kg$ to prevent it from sliding on a plane with an inclination angle $30^{\circ}$ with the horizontal. If the coefficients of static friction and kinetic friction between the block and the plane are $0.4$ and $0.3$ respectively,then the frictional force acting on the block is...... $N$.

Find the work done by friction if a $1 \, kg$ block reaches the end of an inclined plane of length $10 \, m$ and inclination $30^{\circ}$ with constant velocity.

An insect crawls up a hemispherical surface very slowly. The coefficient of friction between the insect and the surface is $1/3$. If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical,the maximum possible value of $\alpha$ so that the insect does not slip is given by

$A$ block takes time $t$ to slide down a plane inclined at $45^\circ$ to the horizontal. If the surface is made smooth (frictionless), the block takes time $t/2$ to slide down the plane. The coefficient of friction between the block and the inclined plane is $\frac{\alpha}{100}$. The value of $\alpha$ is . . . . . . .

$A$ block of weight $1 \,N$ rests on an inclined plane of inclination $\theta$ with the horizontal. The coefficient of friction is $\mu$. The minimum force that has to be applied parallel to the inclined plane to make the body just move up the plane is