A block of mass $M$ is pulled a distance $x$ on horizontal table, the work done by weight is

A curved surface is shown in figure. The portion $BCD$ is free of friction. There are three spherical balls of identical radii and masses. Balls are released from rest one by one from $A$ which is at a slightly greater height than $C$.

With the surface $AB$, ball $1$ has large enough friction to cause rolling down without slipping; ball $2$ has a small friction and ball $3$ has a negligible friction.

$(a)$ For which balls is total mechanical energy conserved ?

$(b)$ Which ball $(s)$ can reach $D$ ?

$(c)$ For ball which do not reach $D$, which of the balls can reach back $A$ ?

A uniform chain of length $L$ and mass $M$ is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. If $g$ is acceleration due to gravity, work required to pull the hanging part on to the table is

A 3.628 kg freight car moving along a horizontal rail road spur track at $7.2\; km/hour$ strikes a bumper whose coil springs experiences a maximum compression of $30 \;cm$ in stopping the car. The elastic potential energy of the springs at the instant when they are compressed $15\; cm$ is [2013]

(a) $12.1 \times 10^4\;J$ (b) $121  \times 10^4\;J$ (c) $1.21 \times 10^4\;J$ (d) $1.21  \times 10^4\;J$