A spring of force constant $k$ is cut in two parts at its one third length. When both the parts are stretched by same amount, the work done in the two parts, will be

The work done in joules in increasing the extension of a spring of stiffness $10\, N/cm$ from $4\, cm$ to $6\, cm$ is:

$10\  m$ 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)

The energy stored in wound watch spring is

Write the dimensional formula of $\frac {k}{m}$.

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: $k_1 < k_2$