The system shown in the figure is in equilibrium and at rest. The spring and string are massless. Now, the string is cut. The acceleration of mass $2m$ and $m$ just after the string is cut will be:

$A$ 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

Two springs $A$ and $B$ having spring constants $K_{A}$ and $K_{B}$ $(K_{A} = 2 K_{B})$ are stretched by applying forces of equal magnitude. If the energy stored in spring $A$ is $E_{A}$,then the energy stored in spring $B$ will be:

$A$ spring of force constant $k$ is cut into three equal parts. The force constant of each part would be

In the setup shown,a $200\, N$ block is supported in equilibrium with the help of strings and a spring. At point $O$,the strings are knotted. The extension in the spring is $4\, cm$. The force constant of the spring is closest to ............ $N/m$ $[g = 10\, m/s^2]$.

Two masses of $1 \, kg$ and $2 \, kg$ respectively are connected by a massless spring as shown in the figure. $A$ force of $20 \, N$ acts on the $2 \, kg$ mass. At the instant when the $1 \, kg$ mass has an acceleration of $10 \, m/s^2$ towards the right,the acceleration of the $2 \, kg$ mass is ......... $m/s^2$.