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 $: 1$)

When a $1.0\,kg$ mass hangs attached to a spring of length $50\,cm$,the spring stretches by $2\,cm$. The mass is pulled down until the length of the spring becomes $60\,cm$. What is the amount of elastic energy stored in the spring in this condition,if $g = 10\,m/s^2$? (in $Joule$)

Two blocks with masses $100 \text{ g}$ and $200 \text{ g}$ are attached to the ends of springs $A$ and $B$ as shown in the figure. The energy stored in spring $A$ is $E$. The energy stored in spring $B$,when the spring constants $k_{A}$ and $k_{B}$ of springs $A$ and $B$ respectively satisfy the relation $4k_{A} = 3k_{B}$,is:

$A$ 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 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:

$A$ spring of force constant $k$ is cut into three equal pieces. If these three pieces are connected in parallel,the force constant of the combination will be