$A$ mechanical system consists of two springs with stiffness coefficients $k_1$ and $k_2$ connected in series. The minimum work to be performed on the system to stretch it by a total displacement $\Delta$ is

$A$ $15\, g$ ball is shot from a spring gun whose spring has a force constant of $600\, N/m$. The spring is compressed by $3\, cm$. The greatest possible velocity of the ball for this compression is ............. $m/s$ $(g = 10\, m/s^2)$.

$A$ spring has a natural length $l$ with one end fixed to the ceiling. The other end is fitted with a smooth ring which can slide on a horizontal rod fixed at distance $l$ below the ceiling. Initially,the spring makes an angle of $60^{\circ}$ with the vertical,when the system is released from rest. Find the angle of the spring with the vertical,when the velocity of the ring reaches half of the maximum velocity,which the ring can attain during the motion.

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,the work done on $S_1$ is more than on $S_2$.
Statement $2$: $k_1 < k_2$.

$A$ 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 of original length $L$ and spring constant $K$ is stretched by a small length $x$. It is further stretched by another small length $y$. Find the work done in the second stretching.