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:

Two plates each of mass $m$ are connected by a massless spring as shown below. $A$ weight $W$ is placed on the upper plate which compresses the spring further. When $W$ is removed,the entire assembly jumps up. The minimum weight $W$ needed for the assembly to jump up when the weight is removed is just more than ...........$m$.

Two massless springs of spring constant $K_1$ and $K_2$ are connected in series,suspended vertically,and a certain mass is attached to the free end. If $e_1$ and $e_2$ are their respective extensions and $f$ is the stretching force,the total extension produced is:

Two identical springs have the same force constant $73.5 \,Nm^{-1}$. The elongation produced in each spring in the three cases shown in Figure-$1$,Figure-$2$,and Figure-$3$ are (given $g=9.8 \,ms^{-2}$):

In the figure,blocks $A$ (mass $2m$) and $B$ (mass $m$) are connected with a string and the system is suspended vertically with the help of a spring. The spring has negligible mass. Find the magnitude of the acceleration of masses $2m$ and $m$ just after the instant when the string is cut.

$A$ 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