$A$ block of mass $1 \, kg$ is projected from the lowest point up along an inclined plane with an angle of inclination $45^{\circ}$ and coefficient of friction $\mu = 0.5$. If $g = 10 \, ms^{-2}$,the retardation experienced by the block is ............. $ms^{-2}$.

$A$ block of mass $m$ rests on a rough inclined plane. The coefficient of friction between the surface and the block is $\mu$. At what angle of inclination $\theta$ of the plane to the horizontal will the block just start to slide down the plane?

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

$A$ board is balanced on a rough horizontal semicircular log. Equilibrium is obtained with the help of the addition of a weight to one of the ends of the board when the board makes an angle $\theta$ with the horizontal. The coefficient of friction between the log and the board is:

$A$ 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

The ratio of acceleration of block $A$ placed on a smooth incline to block $B$ placed on a rough incline is $2:1$. The coefficient of kinetic friction between block $B$ and the incline is .........