A uniform chain of length $L$ and mass $M$ overhangs a horizontal table with its two third part on the table. The friction coefficient between the table and the chain is $\mu$ Find the work done by the friction during the period the chain slips off the table.
 

A block of mass $1 \mathrm{kg}$ is placed at the point $A$ of a rough track shown in figure. If slightly pushed towards right, it stops at the point $B$ of the track. Calculate the work done by the frictional force on the block during its transit from $A$ to $B$.

Shows a spring fixed at the bottom end of an incline of inclination $37°.$ A small block of mass $2 \mathrm{kg}$ starts slipping down the incline from a point $4·8 \mathrm{m}$ away from the spring. The block compresses the spring by $20 \mathrm{cm},$ stops momentarily and then rebounds through a distance of $1 \mathrm{m}$ up the incline. Find

(a) the friction coefficient between the plane and the block

(b) the spring constant of the spring. Take $g=10 \mathrm{m}/{\mathrm{s}}^2$

Consider the situation shown in figure. Initially the spring is unstretched when the system is released from rest. Assuming no friction in the pulley, the maximum elongation of the spring is $\frac{mg}{\mathrm{x}k}$. The value of number $\mathrm{x}$ is:

A block of mass $m$ is attached to two unstretched springs of spring constants $k_1$ and $k_2$ as shown in figure. The block is displaced towards right through a distance $x$ and is released. The speed of the block as it passes through the mean position shown is $\sqrt{\frac{k_1+k_2}{\_}}x$. Fill in the blank.

A block of mass $m$ sliding on a smooth horizontal surface with a velocity $v$ meets a long horizontal spring fixed at one end and having spring constant $k$ as shown in figure. $\sqrt{\frac{am}{bk}}v$ is the maximum compression of the spring. Find the value of $\frac{b}{a}$, here $a \text{and} b$ are integers.