A chain of mass $m$ and length $l$ is hanging freely from edge $A$ (as shown in diagram $I$ ). Calculate the work done to fold it as shown in diagram $(II)$ 

A ring of mass $m$ is attached to a horizontal spring of spring constant $k$ and natural length $l_0$ . Other end of spring is fixed and ring can slide on a smooth horizontal rod as shown. Now the ring is shifted to position $B$ and released, speed of ring when spring attains it's natural length is

A spring of spring constant $ 5 \times 10^3$ $ N/m$  is stretched initially by $5\,cm$ from the unstretched position. Then the work required to stretch it further by another $5\,cm$ is .............. $\mathrm{N-m}$

$A$ $1.0\, kg$ block collides with a horizontal weightless spring of force constant $2.75 Nm^{-1}$ as shown in figure. The block compresses the spring $4.0\, m$ from the rest position. If the coefficient of kinetic friction between the block and horizontal surface is $0.25$, the speed of the block at the instant of collision is ................. $\mathrm{m}/ \mathrm{s}^{-1}$

A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is :

A block of mass $2\,\,kg$ is placed on a rough inclined plane as shown in the figure $(\mu  = 0.2)$ so that it just touches the spring. The block is allowed to move downwards. The spring will be compressed to a maximum of