$A$ massless platform is kept on a light elastic spring as shown in the figure. When a sand particle of mass $0.1 \; kg$ is dropped on the pan from a height of $0.24 \; m$,the particle strikes the pan and the spring is compressed by $0.01 \; m$. From what height should the particle be dropped to cause a compression of $0.04 \; m$ (in $; m$)?

$A$ ball of mass $100 \, g$ is dropped from a height $h = 10 \, cm$ onto a platform fixed at the top of a vertical spring (as shown in the figure). The ball stays on the platform and the platform is depressed by a distance $\frac{h}{2}$. The spring constant is .......... $N \, m^{-1}$. (Use $g = 10 \, m \, s^{-2}$)

$Assertion$ : Graph between potential energy of a spring versus the extension or compression of the spring is a straight line.
$Reason$ : Potential energy of a stretched or compressed spring is proportional to the square of extension or compression.

$A$ spring with spring constant $k$ when stretched through $1 \, cm$,the potential energy is $U$. If it is stretched by $4 \, cm$,the potential energy will be (in $U$)

$A$ 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 $m$)?

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