$A$ 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 springs $A$ and $B$ are fixed at the top and are stretched by $8 \,cm$ and $16 \,cm$ respectively, when loads of $20 \,N$ and $10 \,N$ are suspended at the lower ends. The ratio of the spring constants of the springs $A$ and $B$ is (in $: 1$)

The block $A$ is pushed towards the wall by a distance $x$ and released. The normal reaction $N$ by the vertical wall on the block $B$ versus the compression $x$ in the spring is given by:

$A$ 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?

$A$ 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

When a body is suspended from a spring and released slowly,the extension in the spring is $x$. If the body is released suddenly,the extension in the spring is: