$A$ long spring, when stretched by a distance $x$, has the potential energy $u$. On increasing the stretching to $nx$, the potential energy of the spring will be:

$A$ 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 $g = 10 \, m \, s^{-2}$)

$A$ light spring of length $10 \ cm$ is stretched by $2 \ cm$ when a mass of $20 \ g$ is attached to its end. The mass is pulled until the total length of the spring becomes $14 \ cm$. What is the elastic potential energy stored in the spring (in Joules)?

Two springs with spring constants $K_1 = 1500 \, N/m$ and $K_2 = 3000 \, N/m$ are stretched by the same force. The ratio of potential energy stored in the springs will be

The potential energy of a weightless spring compressed by a distance $a$ is proportional to

$A$ 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 $k$?