If the normal reaction is $R$ and the coefficient of friction is $\mu$,what is the work done against friction in moving a body by a distance $d$ slowly?

$A$ block is kept on a rough horizontal surface. The acceleration of the block increases from $6 \ m/s^2$ to $11 \ m/s^2$ when the horizontal force acting on it increases from $20 \ N$ to $30 \ N$. The coefficient of kinetic friction between the block and the surface is (Acceleration due to gravity $g = 10 \ m/s^2$):

What is the maximum value of the force $F$ such that the block shown in the arrangement does not move (in $N$)? (Given $m = \sqrt{3} \ kg$,$\mu = \frac{1}{2\sqrt{3}}$,$g = 10 \ m/s^2$)

What is the maximum value of the force $F$ such that the block shown in the arrangement does not move? (in $N$)

$A$ 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?

$A$ block is projected with speed $20 \,m/s$ on a rough horizontal surface. The coefficient of friction $(\mu)$ between the surfaces varies with time $(t)$ as shown in the figure. The speed of the body at the end of $4 \,s$ will be ............ $m/s$ $(g = 10 \,m/s^2)$.