$A$ block of mass $m$ moving with speed $v$ compresses a spring through distance $x$ before its speed is halved. What is the value of the spring constant $k$?

$A$ 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 .............. $m$.

If the potential energy of a spring is $V$ on stretching it by $2 \, cm$,then its potential energy when it is stretched by $10 \, cm$ will be

$A$ body of mass $0.15 \ kg$ moving with a velocity of $15 \ ms^{-1}$ comes to rest when it hits a spring that is fixed at the other end. If the force constant of the spring is $1500 \ Nm^{-1}$,then the compression in the spring is: (in $m$)

$A$ spring of spring constant $5 \times 10^3 \, N/m$ is stretched initially by $5 \, cm$ from the unstretched position. Then the work required to stretch it further by another $5 \, cm$ is .............. $J$.

$A$ light elastic spring is placed on a massless platform as shown in the figure. $A$ sand particle of mass $0.1 \ kg$ is dropped onto the spring platform from a height of $0.24 \ m$. The particle sticks to the platform,causing the spring to compress by $0.01 \ m$. From what height should the particle be dropped so that the spring is compressed by $0.04 \ m$ (in $m$)?