When a spring is stretched by $2 \ cm$,the potential energy stored is $U$. If it is stretched by $10 \ cm$,the potential energy stored will be:

To simulate car accidents,auto manufacturers study the collisions of moving cars with mounted springs of different spring constants. Consider a typical simulation with a car of mass $1000 \; kg$ moving with a speed $18.0 \; km/h$ on a smooth road and colliding with a horizontally mounted spring of spring constant $6.25 \times 10^{3} \; N m^{-1}$. What is the maximum compression of the spring in $m$?

$A$ block of mass $100 \ g$ moving at a speed of $2 \ m \ s^{-1}$ compresses a spring through a distance $2 \ cm$ before its speed is halved. Find the spring constant of the spring. (in $N \ m^{-1}$)

The potential energy of a long spring when stretched by $2\,cm$ is $U$. If the spring is stretched by $8\,cm$,the potential energy stored in it will be $.......\,U$.

An elastic spring of unstretched length $L$ and force constant $k$ is stretched by a small length $x$. It is further stretched by another small length $y$. Work done during the second stretching is

$A$ ball of mass $4\, kg$,moving with a velocity of $10\, ms^{-1}$,collides with a spring of length $8\, m$ and force constant $100\, Nm^{-1}$. The length of the compressed spring is $x\, m$. The value of $x$,to the nearest integer,is ........ .