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

If the normal force is doubled, the coefficient of friction is

Abody 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

Which one of the following is not used to reduce friction

A body of mass $10$ kg slides along a rough horizontal surface. The coefficient of friction is $1/\sqrt 3 $. Taking $g = 10\,m/{s^2}$, the least force which acts at an angle of $30^o $ to the horizontal is ...... $N$

A rectangular box lies on a rough inclined surface. The coefficient of friction between the surface and the box is $\mu $. Let the mass of the box be $m$.

$(a)$ At what angle of inclination $\theta $ of the plane to the horizontal will the box just start to slide down the plane ?

$(b)$ What is the force acting on the box down the plane, if the angle of inclination of the plane is increased to $\alpha > \theta $ ?

$(c)$ What is the force needed to be applied upwards along the plane to make the box either remain stationary or just move up with uniform speed ?

$d)$ What is the force needed to be applied upwards along the plane to make the box move up the plane with acceleration $a$ ?