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

$A$ massless spring of force constant $K$ is placed between two blocks of masses $m$ and $M$ on a frictionless table and compressed by an amount $x$. Upon releasing the spring,both blocks move in opposite directions. The blocks lose contact with the spring when it reaches its natural length. The speed of the block of mass $M$ at the moment of separation is:

$A$ block of mass $m$ slides down an inclined plane as shown in the figure and hits a spring at the bottom,causing it to compress. If the spring constant is $K$,what is the maximum compression of the spring?

The potential energy of a certain spring when stretched through a distance $S$ is $10 \, J$. The amount of work (in $J$) that must be done on this spring to stretch it through an additional distance $S$ will be

Show that the law of conservation of mechanical energy is obeyed by pulling or compressing the block tied at the end of a spring.

$Assertion$ : 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.