$A$ 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 ........ .

The work done in stretching a spring of force constant $5 \times 10^3 \ N/m$ from $5 \ cm$ to $10 \ cm$ is ...... $N-m$.

$A$ block of mass $m$ is pushed against a spring with spring constant $k$,which is fixed at one end to a wall. The block can slide on a frictionless table as shown in the figure. If the natural length of the spring is $L_0$ and it is compressed to half its length when the block is released,find the velocity of the block when the spring reaches its natural length.

$A$ spring,when stretched by $2 \,mm$,has a potential energy of $4 \,J$. If it is stretched by $10 \,mm$,its potential energy will be:

The force constants of two springs are $K_1$ and $K_2$. Both are stretched until their elastic potential energies are equal. If the stretching forces applied are $F_1$ and $F_2$,then the ratio $F_1:F_2$ is:

Find the maximum tension in the spring if the spring is initially at its natural length when the block of mass $m$ is released from rest.