A $0.5 \,kg$ block moving at a speed of $12 \,ms ^{-1}$ compresses a spring through a distance $30\, cm$ when its speed is halved. The spring constant of the spring will be $Nm ^{-1}$.

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

Find the maximum tension in the spring if initially spring at its natural length when block is released from rest.

Two springs of spring constants $1500\, N/m$ and $3000\, N/m$ respectively are stretched with the same force. They will have potential energy in the ratio

In stretching a spring by $2\,cm$ energy stored is given by $U,$ then more stretching by $10\,cm$ energy stored will be

$A$ ball of mass $m = 60gm$ is shot with speed $v_0 = 22m/s$ into the barrel of spring gun of mass $M = 240g$ initially at rest on $a$ frictionless surface. The ball sticks in the barrel at the point of maximum compression of the spring. The speed of the spring gun after the ball stops relative to the barrel, is