$A$ $1\, kg$ 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:

$A$ 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 $U$)

$A$ 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.

When an elastic spring is stretched or compressed,does its potential energy increase or decrease?

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

$A$ spring of force constant $800\, N/m$ has an extension of $5\, cm$. The work done in extending it from $5\, cm$ to $15\, cm$ is ............. $J$.