$A$ body is placed on a rough inclined plane of inclination $\theta$. As the angle $\theta$ is increased from $0^o$ to $90^o$,the contact force between the block and the plane

$A$ block of a certain mass is placed on a rough inclined plane. The angle between the plane and the horizontal is $30^{\circ}$. The coefficients of static and kinetic friction between the block and the inclined plane are $0.6$ and $0.5$ respectively. Then,the magnitude of the acceleration of the block is [Take $g = 10 \ ms^{-2}$]

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

An object takes $n$ times as much time to slide down a $45^{\circ}$ rough inclined plane as it takes to slide down a perfectly smooth inclined plane of the same inclination. The coefficient of kinetic friction between the object and the rough incline is given by:

If the coefficient of friction between an ant and the surface is $1/3$,find the maximum value of $\alpha$.

$A$ 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).