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

$A$ block of mass $m$ is pushed against a spring with spring constant $k$ which is attached to a wall. The block slides on a frictionless table as shown in the figure. The natural length of the spring is $\ell_0$ and it is compressed to half of its natural length when the block is released. What will be the final velocity of the block?

Fill in the blank: $A$ spring is stretched by $3 \, cm$,its potential energy is $U_1$. If the spring is stretched by $6 \, cm$,its potential energy stored in it is $U_2 = ...... U_1$.

$A$ ring of mass $m$ is attached to a horizontal spring of spring constant $k$ and natural length $l_0$. The other end of the spring is fixed,and the ring can slide on a smooth horizontal rod as shown. Now,the ring is shifted to position $B$ and released. The speed of the ring when the spring attains its natural length is:

$A$ spring with force constant $k$ is initially stretched by a distance $x$. If it is further stretched by a distance $y$,the work done during the second stretching is.........

$A$ body of mass $0.5 \ kg$ moves with a speed of $1.5 \ m/s$ on a smooth horizontal surface. It hits a massless spring with a force constant $k = 50 \ N/m$. What will be the maximum compression of the spring in $m$?