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 is:

When a long spring of $4 \ cm$ is stretched by $1 \ cm$,the potential energy stored in the spring is $U$. If it is stretched by $4 \ cm$,the potential energy stored in it is (in $U$)

$A$ sphere of mass $m$ is attached to a spring of spring constant $k$ and is held in an unstretched position over an inclined plane as shown in the figure. After letting the sphere go,find the maximum length by which the spring extends,given the sphere only rolls.

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 $m$?

Two masses $m_1 = 2\,kg$ and $m_2 = 5\,kg$ are moving on a frictionless surface with velocities $10\,m/s$ and $3\,m/s$ respectively. An ideal spring with spring constant $K = 1120\,N/m$ is attached to the back of $m_2$. The maximum compression of the spring will be ............... $m$.

$A$ block of mass $m$ initially at rest is dropped from a height $h$ onto a spring of force constant $k$. If the maximum compression in the spring is $x$,then: