$A$ $15\, g$ ball is shot from a spring gun whose spring has a force constant of $600\, N/m$. The spring is compressed by $3\, cm$. The greatest possible velocity of the ball for this compression is ............. $m/s$ $(g = 10\, m/s^2)$.

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

Two springs have spring constants $k_{A}$ and $k_{B}$ such that $k_{A} > k_{B}$. If both springs are stretched by the same extension $x$,the work required will be:

$A$ mechanical system consists of two springs with stiffness coefficients $k_1$ and $k_2$ connected in series. The minimum work to be performed on the system to stretch it by a total displacement $\Delta$ is

$A$ 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 $m$)?

$A$ 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 $cm$.