The upper half of an inclined plane with inclination $\phi$ is perfectly smooth,while the lower half is rough. $A$ body starting from rest at the top will again come to rest at the bottom,if the coefficient of friction for the lower half is given by-

The force required to move a body up a rough inclined plane is double the force required to prevent the body from sliding down the plane. The coefficient of friction, when the angle of inclination of the plane is $60^{\circ}$ is

$A$ body of mass $10\, kg$ is lying on a rough plane inclined at an angle of $30^\circ$ to the horizontal,and the coefficient of friction is $0.5$. The minimum force required to pull the body up the plane is ........ $N$.

$A$ 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).

$A$ rocket is fired vertically from the earth with an acceleration of $2g,$ where $g$ is the gravitational acceleration. On an inclined plane inside the rocket,making an angle $\theta$ with the horizontal,a point object of mass $m$ is kept. The minimum coefficient of friction $\mu_{min}$ between the mass and the inclined surface such that the mass does not move is

$A$ block of mass $m$ is at rest on an inclined plane with an angle of inclination $\theta$ and coefficient of friction $\mu$,as shown in the figure. The frictional force acting on the block is: