$A$ block of mass $m$ is pressed against a vertical wall by a horizontal force of magnitude $mg$. An upward force of magnitude $\frac{mg}{2}$ is also applied to the block. If the block is in equilibrium,the minimum coefficient of friction $\mu$ between the block and the wall is:

$A$ block of mass $5\,kg$ is placed at rest on a table with a rough surface. If a force of $30\,N$ is applied parallel to the surface of the table,the block slides through a distance of $50\,m$ in $10\,s$. Calculate the coefficient of kinetic friction. (Given: $g = 10\,m/s^2$)

$A$ uniform chain of length $L$ is lying on a horizontal table. If the coefficient of friction between the chain and the table top is $\mu$,what is the maximum length of the chain that can hang over the edge of the table without disturbing the rest of the chain on the table?

On a rough horizontal surface,a body of mass $2 \, kg$ is given a velocity of $10 \, m/s$. If the coefficient of friction is $0.2$ and $g = 10 \, m/s^2$,the body will stop after covering a distance of ........ $m$.

$A$ $1\,kg$ block is being pushed against a wall by a force $F = 75\,N$ as shown in the Figure. The coefficient of friction is $0.25.$ The magnitude of acceleration of the block is ........ $m/s^2$. (Take $g = 10\,m/s^2$)

$A$ movable steel plate is placed between fixed steel and brass plates and the stack of plates is subjected to a weight of $100 \ N$ as shown in the figure. The coefficient of kinetic friction for steel on steel is $0.57$ and for steel on brass is $0.44$. Assuming that the entire weight comes onto the stack and that the weight of the plates is negligible in comparison to the applied weight, the force required to move the middle plate (in $N$) is