$A$ spring of force constant $k$ is cut into two equal halves. The force constant of each half is

$A$ spring of force constant $15 \ N/m$ is cut into two pieces. If the ratio of their lengths is $1 : 3$, then the force constant of the smaller piece is . . . . . . $N/m$.

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:

Two blocks $A$ and $B$ of masses $3\,m$ and $m$ respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in the figure. The magnitudes of acceleration of $A$ and $B$ immediately after the string is cut are respectively:

Two springs,$P$ and $Q$,of force constants $k_P$ and $k_Q$ (where $k_Q = k_P / 2$) are stretched by applying forces of equal magnitude. If the energy stored in $Q$ is $E$,then the energy stored in $P$ is:

$A$ block of mass $m$ is released suddenly from the top of a spring with a spring constant $k$. $(i)$ What will be the maximum compression in the spring? $(ii)$ What will be the compression in the spring at the equilibrium position?