If for an inclined plane the coefficient of static friction is $\mu_s = \frac{3}{4}$,then the angle of repose for the inclined plane will be ........ $^o$.

The time taken by a block to slide down a rough inclined plane of angle $30^{\circ}$ is $n=2$ times the time taken to slide down a frictionless inclined plane of the same angle $30^{\circ}$. The coefficient of kinetic friction between the block and the plane is:

Sand is to be piled up on a horizontal ground in the form of a regular cone of a fixed base of radius $R$. The coefficient of static friction between the sand layers is $\mu$. The maximum volume of the sand that can be piled up in the form of a cone without slipping on the ground is

$A$ block of mass $2 \, kg$ rests on a plane inclined at an angle of $30^o$ with the horizontal. The coefficient of friction between the block and the surface is $0.7$. The frictional force acting on the block is . . . . . . $N$.

$A$ small mass slides down an inclined plane of angle $\theta$ with the horizontal. The coefficient of friction is $\mu = \mu_0 x$,where $x$ is the distance through which the mass slides down and $\mu_0$ is a constant. Then,the distance covered by the mass before it stops is:

The time taken by an object to slide down a $45^{\circ}$ rough inclined plane is $n$ times the time it takes to slide down a perfectly smooth $45^{\circ}$ inclined plane. The coefficient of kinetic friction between the object and the inclined plane is: