$A$ mass of $1 \ kg$ falls from a height of $1 \ m$ and lands on a massless platform supported by a spring having spring constant $15 \ N \ m^{-1}$ as shown in the figure. The maximum compression of the spring is. (acceleration due to gravity $= 10 \ m \ s^{-2}$)

To simulate car accidents,auto manufacturers study the collisions of moving cars with mounted springs of different spring constants. Consider a typical simulation with a car of mass $1000 \; kg$ moving with a speed $18.0 \; km/h$ on a smooth road and colliding with a horizontally mounted spring of spring constant $6.25 \times 10^{3} \; N m^{-1}$. What is the maximum compression of the spring in $m$?

$A$ spring of force constant $K$ is first stretched by distance $a$ from its natural length and then further by distance $b$. The work done in stretching the part $b$ is .............

$A$ mass of $0.5\,kg$ moving with a speed of $1.5\,m/s$ on a horizontal smooth surface,collides with a nearly weightless spring of force constant $k = 50\,N/m$. The maximum compression of the spring would be ............. $m$.

$A$ spring is stretched by a distance $s$,and the potential energy stored in it is $10 \ J$. What is the work done to stretch the spring by an additional distance $s$ (in $J$)?

$A$ spring has a natural length $l$ with one end fixed to the ceiling. The other end is fitted with a smooth ring which can slide on a horizontal rod fixed at distance $l$ below the ceiling. Initially, the spring makes an angle of $60^{\circ}$ with the vertical, when the system is released from rest. Find the angle of the spring with the vertical, when the velocity of the ring reaches half of the maximum velocity, which the ring can attain during the motion.