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 $.......\,U$.

$A$ body of mass $0.1 \ kg$ moving with a velocity of $10 \ m/s$ hits a spring (fixed at the other end) of force constant $1000 \ N/m$ and comes to rest after compressing the spring. The compression of the spring is .............. $m$.

$A$ mass of $0.5\,kg$ moving with a speed of $1.5\,m/s$ on a horizontal smooth surface,collides with a nearly weightless spring of force constant $k = 50\,N/m$. The maximum compression of the spring would be ............. $m$.

$A$ smooth track extends to a horizontal part as shown in the figure. $A$ spring with a force constant of $400 \ N/m$ is firmly attached to one end of this horizontal part. $A$ mass of $40 \ g$ is released from a height of $4.9 \ m$. Calculate the compression in the spring in $cm$.

$A$ spring with spring constant $k$ is extended from $x = 0$ to $x = x_1$. The work done will be

The spring is initially in an unstretched condition. It is first stretched by a length $x$ and the work done is $W_1$. Then again it is stretched by a further length $x$ such that the total extension becomes $2x$. The work done in this second step is $W_2$. The value of $W_2$ is given by