When a $1.0\,kg$ mass hangs attached to a spring of length $50\,cm$,the spring stretches by $2\,cm$. The mass is pulled down until the length of the spring becomes $60\,cm$. What is the amount of elastic energy stored in the spring in this condition,if $g = 10\,m/s^2$? (in $Joule$)

$A$ spring has length $l$ and force constant $K$. If it is cut into two springs of length $l_1$ and $l_2$ such that $l_1 = n l_2$ ($n$ is an integer). The force constant of the spring of length $l_2$ is

Two balls $A$ and $B$ of masses $100 \ gm$ and $250 \ gm$ are connected by a stretched massless spring and placed on a smooth table. When the balls are released simultaneously,the initial acceleration of ball $B$ is $10 \ cm/s^2$ towards the west. Find the magnitude and direction of the initial acceleration of ball $A$.

An ideal spring with spring-constant $K$ is hung from the ceiling and a block of mass $M$ is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is

The spring extends by $x$ on loading,then the energy stored by the spring is: (if $T$ is the tension in the spring and $k$ is the spring constant)

$A$ body of mass $m$ is suspended from an ideal spring of force constant $k$. The expected change in the position of the body due to an additional force $F$ acting vertically downwards is