When a $1.0\,kg$ mass hangs attached to a spring of length $50 cm$, the spring stretches by $2 \,cm$. The mass is pulled down until the length of the spring becomes $60\, cm.$ What is the amount of elastic energy stored in the spring in this condition, if $g = 10 m/s^{2}$ …………. $\mathrm{Joule}$

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 $Nm ^{-1}$.

A ring of mass $m$ is attached to a horizontal spring of spring constant $k$ and natural length $l_0$ . Other end of spring is fixed and ring can slide on a smooth horizontal rod as shown. Now the ring is shifted to position $B$ and released, speed of ring when spring attains it's natural length is

A spring of force constant $k$ is cut into three equal pieces. If these three pieces are connected in parallel the force constant of the combination will be

Give the example of variable force. Write the formula of Hook’s law.