$A$ 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

The tension in the spring is ............ $N$.

In the figure,blocks $A$ (mass $2m$) and $B$ (mass $m$) are connected with a string and the system is suspended vertically with the help of a spring. The spring has negligible mass. Find the magnitude of the acceleration of masses $2m$ and $m$ just after the instant when the string is cut.

If a spring is extended to length $l,$ then according to Hooke's law,

$A$ massless spring gets elongated by an amount $x_1$ under a tension of $5 \ N$. Its elongation is $x_2$ under a tension of $7 \ N$. For an elongation of $(5x_1 - 2x_2)$,the tension in the spring will be: (in $N$)

Two springs $A$ and $B$ having spring constants $K_{A}$ and $K_{B}$ $(K_{A} = 2 K_{B})$ are stretched by applying forces of equal magnitude. If the energy stored in spring $A$ is $E_{A}$,then the energy stored in spring $B$ will be: