Two masses of $10\, kg$ and $20\, kg$ respectively are connected by a massless spring as shown in the figure. $A$ force of $200\, N$ acts on the $20\, kg$ mass. At the instant when the $10\, kg$ mass has an acceleration of $12\, m\, s^{-2}$,the acceleration of the $20\, kg$ mass is ...... $m\, s^{-2}$.

$A$ spring of length $l$ has a force constant $k$. When a weight $W$ is attached to it,the extension produced is $x$. If the spring is cut into two equal parts and these parts are connected in parallel to support the same weight $W$,what will be the new extension?

Two blocks are connected by a spring. The combination is suspended,at rest,from a string attached to the ceiling,as shown in the figure. The string breaks suddenly. Immediately after the string breaks,what is the initial downward acceleration of the upper block of mass $2m$?

Two light vertical springs with equal natural lengths and spring constants $k_1$ and $k_2$ are separated by a distance $l$. Their upper ends are fixed to the ceiling and their lower ends to the ends $A$ and $B$ of a light horizontal rod $AB$. $A$ vertical downwards force $F$ is applied at point $C$ on the rod. $AB$ will remain horizontal in equilibrium if the distance $AC$ is

The figure shows two cases. In the first case,a spring (spring constant $K$) is pulled by two equal and opposite forces $F$ at both ends. In the second case,it is pulled by a force $F$ at one end while the other end is fixed. The extensions $(x)$ in the springs will be:

Two springs having spring constants $k_1$ and $k_2$ are connected in series,their resultant spring constant is $2 \text{ unit}$. If they are connected in parallel,their resultant spring constant is $9 \text{ unit}$. Find the values of $k_1$ and $k_2$.