Consider a block kept on an inclined plane (inclined at $45^{\circ}$) as shown in the figure. If the force required to just push it up the incline is $2$ times the force required to just prevent it from sliding down,the coefficient of friction between the block and inclined plane $(\mu)$ is equal to

$A$ uniform chain of length $L$ hangs partly from a table and is kept in equilibrium by friction. If the maximum length of the chain that can hang without slipping is $l$,then the coefficient of friction between the table and the chain is:

$A$ block of mass $m$ is stationary on a rough plane of mass $M$ inclined at an angle $\theta$ to the horizontal,while the whole setup is accelerating upwards at an acceleration $a$. If the coefficient of friction between the block and the plane is $\mu$,then the force that the plane exerts on the block is

$A$ block starts moving up an inclined plane of inclination $30^{\circ}$ with an initial velocity of $v_{0}$. It comes back to its initial position with velocity $\frac{v_{0}}{2}$. The value of the coefficient of kinetic friction between the block and the inclined plane is close to $\frac{I}{1000}$. The nearest integer to $I$ is......

The coefficient of friction between a body and the surface of an inclined plane at $45^o$ is $0.5$. If $g = 9.8\,m/s^2$,the acceleration of the body downwards in $m/s^2$ is

$A$ body of mass $2\,kg$ slides down with an acceleration of $3\,m/s^2$ on a rough inclined plane having a slope of $30^o$. The external force required to take the same body up the plane with the same acceleration will be ........ $N$ $(g = 10\,m/s^2)$.