$A$ 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 $cm$.

$A$ $1\, kg$ block moves towards a light spring with a velocity of $8\, m/s$. When the spring is compressed by $3\, m$,its momentum becomes half of the original momentum. The spring constant of the spring is:

$A$ 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

Work done on a certain spring when it is stretched to $1 \text{ mm}$ from its mean position is $10 \text{ J}$. The amount of work that must be done on the spring to stretch it further by $1 \text{ mm}$ is: (in $\text{ J}$)

Statement-$1$ and Statement-$2$ are given. Two springs $S_1$ and $S_2$ have force constants $k_1$ and $k_2$ respectively,where $k_1 < k_2$. They are stretched by the same force $F$. It is found that the work done on spring $S_1$ is greater than the work done on spring $S_2$.
Statement-$1$: If stretched by the same force,the work done on $S_1$ is greater than the work done on $S_2$.
Statement-$2$: $k_1 < k_2$.