The potential energy of a long spring when stretched by $2\,cm$ is $U$. If the spring is stretched by $8\,cm$, potential energy stored in it will be $.......\,U$

$10\  m$ is the total mass of a cannon that includs  all shell. Initial cannon is moving with velocity $10\  m$ is along a horizontal frictionless path. If cannon fires $'n$' shells of mass $m$ in the direction of motion of the cannon one by one with velocity $u$ with respect to ground. (neglect any friction force)

Two blocks $A$ and $B$ of mass $m$ and $2\, m$ respectively are connected by a massless spring of force constant $k$. They are placed on a smooth horizontal plane. Spring is stretched by an amount $x$ and then released. The relative velocity of the blocks when the spring comes to its natural length is :-

The pointer reading v/s load graph for a spring balance is as given in the figure. The spring constant is ........ $ kg/cm$

As shown in figure there is a spring block system. Block of mass $500\,g$ is pressed against a horizontal spring fixed at one end to compress the spring through $5.0\,cm$ . The spring constant is $500\,N/m$ . When released, calculate the distance where it will hit the ground $4\,m$ below the spring ? $(g = 10\,m/s^2)$

This question has Statement $1$ and Statement $2$. Of the four choices given after the Statements, choose the one that best describes the two Statements.

If two springs $S_1$ and $S_2$ of force constants $k_1$ and $k_2$, respectively, are stretched by the same force, it is found that more work is done on spring $S_1$ than on spring $S_2$.
STATEMENT 1 : If stretched by the same amount work
done on $S_1$, Work done on $S_1$ is more than $S_2$
STATEMENT2: $k_1 < k_2$