$A$ long spring, when stretched by a distance $x$, has the potential energy $u$. On increasing the stretching to $nx$, the potential energy of the spring will be:

Two springs with spring constants $1500 \ N/m$ and $3000 \ N/m$ respectively are stretched by the same force. What is the ratio of their potential energies?

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,the work done on $S_1$ is more than on $S_2$.
Statement $2$: $k_1 < k_2$.

$A$ block of mass $M$ moving on a frictionless horizontal surface collides with a spring of spring constant $K$, as shown in the figure. If the spring compresses by a length $L$, then the maximum momentum of the block is:

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 $S_1$ will be more than that on $S_2$.
Statement $-2$: $k_1 < k_2$.

$A$ block of mass $m$ is hung vertically from an elastic thread of force constant $\frac{2mg}{a}$. Initially,the thread is at its natural length and the block is allowed to fall freely. The work done on the block by the Earth when it passes through the equilibrium position will be: