$A$ block of mass $100 \ g$ moving at a speed of $2 \ m \ s^{-1}$ compresses a spring through a distance $2 \ cm$ before its speed is halved. Find the spring constant of the spring. (in $N \ m^{-1}$)

When a spring is stretched by $2 \ cm$,the potential energy stored is $U$. If it is stretched by $10 \ cm$,the potential energy stored will be:

$A$ 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.

$A$ block of weight $W$ moving with velocity $v$ on a frictionless horizontal surface hits a spring of force constant $k$. The maximum compression in the spring will be at a distance of .........

$A$ sphere of mass $m$ is attached to a spring of spring constant $k$ and is held in an unstretched position over an inclined plane as shown in the figure. After letting the sphere go,find the maximum length by which the spring extends,given the sphere only rolls.

$A$ block of mass $M$ moves on a frictionless horizontal surface and collides with a spring of spring constant $k$. The spring is compressed by a length $L$. What is the maximum momentum of the block after the collision?