$A$ spring with $10$ coils has spring constant $k$. It is exactly cut into two halves,then each of these new springs will have a spring constant

$A$ spring of force constant $k$ is cut into two pieces such that one piece is three times the length of the other. The longer piece will have a force constant of

$A$ spring of force constant $k$ is cut into two equal halves. The force constant of each half 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 $g=9.8 \,ms^{-2}$):

Find the acceleration of $3\,kg$ mass when the acceleration of $2\,kg$ mass is $2\,ms^{-2}$ as shown in the figure.

Two light vertical springs with equal natural lengths and spring constants $k_1$ and $k_2$ are separated by a distance $l$. Their upper ends are fixed to the ceiling and their lower ends to the ends $A$ and $B$ of a light horizontal rod $AB$. $A$ vertical downwards force $F$ is applied at point $C$ on the rod. $AB$ will remain horizontal in equilibrium if the distance $AC$ is