When a $4\, kg$ mass is hung vertically on a light spring that obeys Hooke's law,the spring stretches by $2\, cm$. The work required to be done by an external agent in stretching this spring by $5\, cm$ will be ......... $J$ $(g = 9.8\, m/s^2)$.

This question has Statement $-1$ and Statement $-2$. Of the four choices given after the statements,choose the one that best describes the two statements.
If two springs $S_1$ and $S_2$ of force constants $k_1$ and $k_2$,respectively,are stretched by the same force,it is found that more work is done on spring $S_1$ than on spring $S_2$.
Statement $-1$: If stretched by the same amount,work done on $S_1$ will be more than that on $S_2$.
Statement $-2$: $k_1 < k_2$.

Find the maximum tension in the spring if the spring is initially at its natural length when the block of mass $m$ is released from rest.

$A$ body of mass $0.15 \ kg$ moving with a velocity of $15 \ ms^{-1}$ comes to rest when it hits a spring that is fixed at the other end. If the force constant of the spring is $1500 \ Nm^{-1}$,then the compression in the spring is: (in $m$)

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

$A$ spring with spring constant $k$ when stretched through $1 \, cm$,the potential energy is $U$. If it is stretched by $4 \, cm$,the potential energy will be (in $U$)