$A$ spring of spring constant $5 \times 10^3 \, N/m$ is stretched initially by $5 \, cm$ from the unstretched position. Then the work required to stretch it further by another $5 \, cm$ is .............. $J$.

$A$ smooth track extends to a horizontal part as shown in the figure. $A$ spring with a force constant of $400 \ N/m$ is firmly attached to one end of this horizontal part. $A$ mass of $40 \ g$ is released from a height of $4.9 \ m$. Calculate the compression in the spring in $cm$.

$Assertion$ : Graph between potential energy of a spring versus the extension or compression of the spring is a straight line.
$Reason$ : Potential energy of a stretched or compressed spring is proportional to the square of extension or compression.

$A$ car of mass $1000 \,kg$ having a velocity of $10 \,ms^{-1}$ collides with a horizontally mounted spring. If the spring constant is $4000 \,Nm^{-1}$, then the maximum compression of the spring is: (in $\,m$)

The potential energy of a spring...

Statement-$1$ and Statement-$2$ are given. Two springs $S_1$ and $S_2$ have force constants $k_1$ and $k_2$ respectively,where $k_1 < k_2$. They are stretched by the same force $F$. It is found that the work done on spring $S_1$ is greater than the work done on spring $S_2$.
Statement-$1$: If stretched by the same force,the work done on $S_1$ is greater than the work done on $S_2$.
Statement-$2$: $k_1 < k_2$.