$A$ child weighing $25$ kg slides down a rope hanging from the branch of a tall tree. If the force of friction acting against him is $2$ $N$,the acceleration of the child is ........ $m/s^2$. (Take $g = 9.8$ $m/s^2$)

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

$A$ 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 $g = 10 \ ms^{-2}$]

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:

The tension $T$ in the string shown in the figure is: