$A$ block of mass $m$ moving at a speed $v$ compresses a spring through a distance $x$ before its speed becomes one fourth. Find the spring constant of the spring.

The system of the wedge and the block connected by a massless spring as shown in the figure is released with the spring in its natural length. Friction is absent. The maximum elongation in the spring will be:

If a spring extends by $x$ on loading,then the energy stored in the spring is (where $T$ is the tension in the spring and $K$ is the spring constant):

$K$ is the force constant of a spring. The work done in increasing its extension from $l_1$ to $l_2$ will be

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 ............... $m$.

$A$ 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 $m$)?