$A$ uniform spring of force constant $k$ is cut into two pieces,the lengths of which are in the ratio $1 : 2$. The ratio of the force constants of the shorter and the longer pieces is

Two identical springs have the same force constant $73.5 \,Nm^{-1}$. The elongation produced in each spring in the three cases shown in Figure-$1$,Figure-$2$,and Figure-$3$ are (given $g=9.8 \,ms^{-2}$):

Natural length of a spring is $60\, cm$,and its spring constant is $4000\, N/m$. $A$ mass of $20\, kg$ is hung from it. The extension produced in the spring is,.......$cm$ (Take $g = 9.8\, m/s^2$)

The potential energy of a long spring when it is stretched by $3 \ cm$ is $U$. If the spring is stretched by $9 \ cm$,the potential energy stored in it will be: (in $U$)

The length of a spring is $l$ and its force constant is $k$. When a weight $W$ is suspended from it,its length increases by $x$. If the spring is cut into two equal parts and put in parallel and the same weight $W$ is suspended from them,then the extension will be

Two springs having spring constants $k_1$ and $k_2$ are connected in series,their resultant spring constant is $2 \text{ unit}$. If they are connected in parallel,their resultant spring constant is $9 \text{ unit}$. Find the values of $k_1$ and $k_2$.