Two springs with spring constants $1500 \ N/m$ and $3000 \ N/m$ respectively are stretched by the same force. What is the ratio of their potential energies?

$A$ spring with a spring constant of $5 \times 10^3 \ N/m$ is initially in its natural state. It is stretched by $5 \ cm$. How much work is required to stretch it by another $5 \ cm$?

$A$ body of mass $0.1 \ kg$ moving with a velocity of $10 \ m/s$ hits a spring (fixed at the other end) of force constant $1000 \ N/m$ and comes to rest after compressing the spring. The compression of the spring is .............. $m$.

Fill in the blank: $A$ spring is stretched by $3 \, cm$,its potential energy is $U_1$. If the spring is stretched by $6 \, cm$,its potential energy stored in it is $U_2 = ...... U_1$.

$A$ 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:

$A$ block of mass $100 \ g$ moving at a speed of $2 \ m \ s^{-1}$ compresses a spring through a distance $2 \ cm$ before its speed is halved. Find the spring constant of the spring. (in $N \ m^{-1}$)